Pub Date : 2025-10-30DOI: 10.1016/j.matcom.2025.10.031
Chun-Hsien Li, Chang-Yuan Cheng
The human lymphatic organs are the primary sites where HIV infection occurs and are interconnected within the body in specific structures. These organs are closely linked within the entire lymphatic system, which can increase the risk of HIV infection. The increased interactions between cells in these organs can affect the overall behavior of the virus. When considering these interconnected lymphatic organs as simplicial structures, the entire system becomes a complex network. To study how high-order infections impact viral dynamics, we simplify the network system to a mean-field equation that describes coordinated viral dynamics across multiple infection sites. Even the simplified model may display a backward bifurcation, leading to bistable dynamics. This means that a mild initial infection may disappear, but a severe initial infection can cause the virus to persist. We study the characteristic equations to examine the local stability of the infection-free equilibrium. The equilibria’s global stabilities are demonstrated using the Poincaré–Bendixson theorem for three-dimensional competitive systems and the theory of second compound equations. Furthermore, the complex interactions among lymphatic organs can result in periodic viral dynamics. We conduct numerical simulations of the mean-field equation and the entire network system to illustrate the bistable viral dynamics resulting from backward bifurcation and periodic viral dynamics.
{"title":"Within-host virus infections through high-order interactions","authors":"Chun-Hsien Li, Chang-Yuan Cheng","doi":"10.1016/j.matcom.2025.10.031","DOIUrl":"10.1016/j.matcom.2025.10.031","url":null,"abstract":"<div><div>The human lymphatic organs are the primary sites where HIV infection occurs and are interconnected within the body in specific structures. These organs are closely linked within the entire lymphatic system, which can increase the risk of HIV infection. The increased interactions between cells in these organs can affect the overall behavior of the virus. When considering these interconnected lymphatic organs as simplicial structures, the entire system becomes a complex network. To study how high-order infections impact viral dynamics, we simplify the network system to a mean-field equation that describes coordinated viral dynamics across multiple infection sites. Even the simplified model may display a backward bifurcation, leading to bistable dynamics. This means that a mild initial infection may disappear, but a severe initial infection can cause the virus to persist. We study the characteristic equations to examine the local stability of the infection-free equilibrium. The equilibria’s global stabilities are demonstrated using the Poincaré–Bendixson theorem for three-dimensional competitive systems and the theory of second compound equations. Furthermore, the complex interactions among lymphatic organs can result in periodic viral dynamics. We conduct numerical simulations of the mean-field equation and the entire network system to illustrate the bistable viral dynamics resulting from backward bifurcation and periodic viral dynamics.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 613-633"},"PeriodicalIF":4.4,"publicationDate":"2025-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145465692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-30DOI: 10.1016/j.matcom.2025.10.032
Jinling Wang , Shuoshuo Li , Kai Wang , Qiang Li , Wenyu Tao
This article considers the design problem of an asynchronous dissipative filter for a class of Takagi–Sugeno (T–S) fuzzy singular positive delay systems subject to state-dependent switching, quantization effects, and missing measurements. Firstly, the quantization mechanism is introduced to reduce data conflicts and transmission costs. Secondly, the phenomena of missing measurements and asynchronous switching are also taken into account to design a filter that is more aligned with reality. The focus of this article is on the design of a filter that can ensure the positivity, causality, regularity, stochastic stability, and --dissipativity of the filtering error system in the simultaneous presence of quantization effects, probabilistic missing measurements, and asynchronous switching phenomena. Additionally, the related sufficient criteria are presented in the manner of linear programming (LP) and the design method of filter gain matrices is also specifically provided. Finally, the effectiveness and correctness of the proposed results are demonstrated through two numerical examples.
{"title":"Asynchronous dissipative filtering for T–S fuzzy singular switched positive delay systems with quantization effects and missing measurements","authors":"Jinling Wang , Shuoshuo Li , Kai Wang , Qiang Li , Wenyu Tao","doi":"10.1016/j.matcom.2025.10.032","DOIUrl":"10.1016/j.matcom.2025.10.032","url":null,"abstract":"<div><div>This article considers the design problem of an asynchronous dissipative filter for a class of Takagi–Sugeno (T–S) fuzzy singular positive delay systems subject to state-dependent switching, quantization effects, and missing measurements. Firstly, the quantization mechanism is introduced to reduce data conflicts and transmission costs. Secondly, the phenomena of missing measurements and asynchronous switching are also taken into account to design a filter that is more aligned with reality. The focus of this article is on the design of a filter that can ensure the positivity, causality, regularity, stochastic stability, and <span><math><mrow><mo>(</mo><mi>ζ</mi><mo>,</mo><mi>η</mi><mo>)</mo></mrow></math></span>-<span><math><mi>α</mi></math></span>-dissipativity of the filtering error system in the simultaneous presence of quantization effects, probabilistic missing measurements, and asynchronous switching phenomena. Additionally, the related sufficient criteria are presented in the manner of linear programming (LP) and the design method of filter gain matrices is also specifically provided. Finally, the effectiveness and correctness of the proposed results are demonstrated through two numerical examples.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 596-612"},"PeriodicalIF":4.4,"publicationDate":"2025-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-30DOI: 10.1016/j.matcom.2025.10.033
Qiwei Feng , Bin Han , Michael Neilan
<div><div>In this paper, we consider the Stokes problem with Dirichlet boundary conditions and the constant kinematic viscosity <span><math><mi>ν</mi></math></span> in an axis-aligned domain <span><math><mi>Ω</mi></math></span>. We decouple the velocity <span><math><mi>u</mi></math></span> and pressure <span><math><mi>p</mi></math></span> by deriving a novel biharmonic equation in <span><math><mi>Ω</mi></math></span> and third-order boundary conditions on <span><math><mrow><mi>∂</mi><mi>Ω</mi></mrow></math></span>. In contrast to the fourth-order streamfunction approach, our formulation does not require <span><math><mi>Ω</mi></math></span> to be simply connected. For smooth velocity fields <span><math><mi>u</mi></math></span> in two dimensions, we explicitly construct a finite difference method (FDM) with sixth-order consistency to approximate <span><math><mi>u</mi></math></span> at all relevant grid points: interior points, boundary side points, and boundary corner points. The resulting scheme yields two linear systems <span><math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><msubsup><mrow><mi>u</mi></mrow><mrow><mi>h</mi></mrow><mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></msubsup><mo>=</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math></span> and <span><math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><msubsup><mrow><mi>u</mi></mrow><mrow><mi>h</mi></mrow><mrow><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mrow></msubsup><mo>=</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>, where <span><math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> are constant matrices, and <span><math><mrow><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> are independent of the pressure <span><math><mi>p</mi></math></span> and the kinematic viscosity <span><math><mi>ν</mi></math></span>. Thus, the proposed method is pressure- and viscosity-robust. To accommodate velocity fields with less regularity, we modify the FDM by removing singular terms in the right-hand side vectors. Once the discrete velocity is computed, we apply a sixth-order finite difference operator to first approximate the pressure gradient locally, and then calculate the pressure itself locally with sixth-order accuracy, both without solving any additional linear systems. In our numerical experiments, we test both smooth and non-smooth solutions <span><math><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>p</mi><mo>)</mo></mrow></math></span> in a square domain, a triply connected domain, and an <span><math><mi>L</mi></math></span>-shaped domain in two dimensions. The results confirm sixth-order convergence of the velocity, pressure gradient, and pressure in the <span><math><msub><mrow><mi>ℓ
{"title":"A high-order, pressure-robust, and decoupled finite difference method for the Stokes problem","authors":"Qiwei Feng , Bin Han , Michael Neilan","doi":"10.1016/j.matcom.2025.10.033","DOIUrl":"10.1016/j.matcom.2025.10.033","url":null,"abstract":"<div><div>In this paper, we consider the Stokes problem with Dirichlet boundary conditions and the constant kinematic viscosity <span><math><mi>ν</mi></math></span> in an axis-aligned domain <span><math><mi>Ω</mi></math></span>. We decouple the velocity <span><math><mi>u</mi></math></span> and pressure <span><math><mi>p</mi></math></span> by deriving a novel biharmonic equation in <span><math><mi>Ω</mi></math></span> and third-order boundary conditions on <span><math><mrow><mi>∂</mi><mi>Ω</mi></mrow></math></span>. In contrast to the fourth-order streamfunction approach, our formulation does not require <span><math><mi>Ω</mi></math></span> to be simply connected. For smooth velocity fields <span><math><mi>u</mi></math></span> in two dimensions, we explicitly construct a finite difference method (FDM) with sixth-order consistency to approximate <span><math><mi>u</mi></math></span> at all relevant grid points: interior points, boundary side points, and boundary corner points. The resulting scheme yields two linear systems <span><math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><msubsup><mrow><mi>u</mi></mrow><mrow><mi>h</mi></mrow><mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></msubsup><mo>=</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math></span> and <span><math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><msubsup><mrow><mi>u</mi></mrow><mrow><mi>h</mi></mrow><mrow><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mrow></msubsup><mo>=</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>, where <span><math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> are constant matrices, and <span><math><mrow><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> are independent of the pressure <span><math><mi>p</mi></math></span> and the kinematic viscosity <span><math><mi>ν</mi></math></span>. Thus, the proposed method is pressure- and viscosity-robust. To accommodate velocity fields with less regularity, we modify the FDM by removing singular terms in the right-hand side vectors. Once the discrete velocity is computed, we apply a sixth-order finite difference operator to first approximate the pressure gradient locally, and then calculate the pressure itself locally with sixth-order accuracy, both without solving any additional linear systems. In our numerical experiments, we test both smooth and non-smooth solutions <span><math><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>p</mi><mo>)</mo></mrow></math></span> in a square domain, a triply connected domain, and an <span><math><mi>L</mi></math></span>-shaped domain in two dimensions. The results confirm sixth-order convergence of the velocity, pressure gradient, and pressure in the <span><math><msub><mrow><mi>ℓ","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 634-649"},"PeriodicalIF":4.4,"publicationDate":"2025-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145465690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-29DOI: 10.1016/j.matcom.2025.10.021
Ander Ordono , Ignacio Peñarrocha-Alós , Alain Sanchez-Ruiz , Francisco Javier Asensio
The grid forming inverter plays a key role in standalone power systems, where it must generate a stable and stiff voltage for the elements connected to the grid. One of the most common control structures to achieve the voltage source behavior is the cascaded voltage–current controller in synchronous reference frame. However, conventional tuning strategies do not ensure a robust performance of the voltage controller when delays and bandwidth separation are not negligible. To solve this problem, this work proposes a design and optimization methodology based on bilinear matrix inequalities optimization. This approach ensures the robustness of the voltage control on a wide operational range, while meeting different constraints, such as the bandwidth or the decay rate of the system response. The proposed methodology is not limited to conventional control structures, based on decoupled PI regulators and feedforward terms on each of the axes of the synchronous reference frame. Instead, additional terms or degrees of freedom can be added to boost the performance without increasing the tuning complexity. Simulations show that the proposed controller, along with the tuning methodology, can enhance system robustness with minimal impact on the dynamic response.
{"title":"Flexible voltage controller and tuning method for robust operation of standalone grid forming converters","authors":"Ander Ordono , Ignacio Peñarrocha-Alós , Alain Sanchez-Ruiz , Francisco Javier Asensio","doi":"10.1016/j.matcom.2025.10.021","DOIUrl":"10.1016/j.matcom.2025.10.021","url":null,"abstract":"<div><div>The grid forming inverter plays a key role in standalone power systems, where it must generate a stable and stiff voltage for the elements connected to the grid. One of the most common control structures to achieve the voltage source behavior is the cascaded voltage–current controller in synchronous reference frame. However, conventional tuning strategies do not ensure a robust performance of the voltage controller when delays and bandwidth separation are not negligible. To solve this problem, this work proposes a design and optimization methodology based on bilinear matrix inequalities optimization. This approach ensures the robustness of the voltage control on a wide operational range, while meeting different constraints, such as the bandwidth or the decay rate of the system response. The proposed methodology is not limited to conventional control structures, based on decoupled PI regulators and feedforward terms on each of the axes of the synchronous reference frame. Instead, additional terms or degrees of freedom can be added to boost the performance without increasing the tuning complexity. Simulations show that the proposed controller, along with the tuning methodology, can enhance system robustness with minimal impact on the dynamic response.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 890-907"},"PeriodicalIF":4.4,"publicationDate":"2025-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145424756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-27DOI: 10.1016/j.matcom.2025.10.030
Syeda Sarwat Kazmi , Adil Jhangeer , Muhammad Bilal Riaz
The objective of this research is to explore the dynamics of the shallow water wave equation in extended (3+1) dimensions. This equation is employed to represent atmospheric and oceanic turbulence from various standpoints. Utilizing a multiple exp-function technique, various solitary wave configurations in the form of 1-wave, 2-wave, and 3-wave are generated successfully. This approach is especially advantageous for extracting multisolitons without the need of bilinear forms. To visually illustrate and demonstrate the solutions, they are represented graphically using 3D, 2D, and density plots. Additionally, a qualitative nature of the dynamical system is conducted using bifurcation. Subsequently, an outward force is implemented to the model to create a disturbance, resulting in a modified planar system. The chaotic phenomenon in the modified system is confirmed through various tools designed for chaos detection. Further study is carried out on the model’s sensitivity under three different initial conditions, confirming that the system remains stable and does not exhibit high sensitivity. A newly introduced bidirectional scatter plot approach is employed to perform a comparative analysis of solution behaviors, effectively highlighting overlapping regions and distinctions within their solution spaces through data points, showcasing its innovative contribution. The results of this study are both intriguing and make a notable impact on the area of soliton specifically, as well as on the broader field of mathematical physics.
{"title":"Data-driven approach to shallow water equation in ocean engineering: Multi-soliton solutions, chaos, and sensitivity analysis","authors":"Syeda Sarwat Kazmi , Adil Jhangeer , Muhammad Bilal Riaz","doi":"10.1016/j.matcom.2025.10.030","DOIUrl":"10.1016/j.matcom.2025.10.030","url":null,"abstract":"<div><div>The objective of this research is to explore the dynamics of the shallow water wave equation in extended (3+1) dimensions. This equation is employed to represent atmospheric and oceanic turbulence from various standpoints. Utilizing a multiple exp-function technique, various solitary wave configurations in the form of 1-wave, 2-wave, and 3-wave are generated successfully. This approach is especially advantageous for extracting multisolitons without the need of bilinear forms. To visually illustrate and demonstrate the solutions, they are represented graphically using 3D, 2D, and density plots. Additionally, a qualitative nature of the dynamical system is conducted using bifurcation. Subsequently, an outward force is implemented to the model to create a disturbance, resulting in a modified planar system. The chaotic phenomenon in the modified system is confirmed through various tools designed for chaos detection. Further study is carried out on the model’s sensitivity under three different initial conditions, confirming that the system remains stable and does not exhibit high sensitivity. A newly introduced bidirectional scatter plot approach is employed to perform a comparative analysis of solution behaviors, effectively highlighting overlapping regions and distinctions within their solution spaces through data points, showcasing its innovative contribution. The results of this study are both intriguing and make a notable impact on the area of soliton specifically, as well as on the broader field of mathematical physics.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 573-595"},"PeriodicalIF":4.4,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study explores the nonlinear -dimensional double-chain deoxyribonucleic acid (DNA) model, which plays a central role in fundamental biological processes such as replication, transcription, and translation. Utilizing the -expansion method, we derive new exact solutions in the domain of hyperbolic and trigonometric functions. Various soliton structures, such as kink, singular, and singular periodic solitons, are constructed and illustrated through 3D, density, and 2D profiles by means of suitable parameter choices. A qualitative analysis is carried out using the concepts of bifurcation and chaos theory to gain deeper insights. A parameter-dependent bifurcation analysis reveals how minute alterations in parameters can instigate significant fluctuations in system stability. More specifically, a perturbation term is introduced to investigate chaotic responses, which are verified by different detecting tools, Kaplan–Yorke dimension and multistability. To further emphasize the dynamic nature of the model, sensitivity analysis is performed under three distinct initial conditions. These findings expand our understanding of the nonlinear nature of DNA systems and provide fresh perspectives on their stability and complexity.
{"title":"Dynamical observations and range of diverse soliton profiles for a nonlinear double-chain deoxyribonucleic acid model","authors":"Ayesha Ejaz , Zeeshan Amjad , Nauman Raza , Patricia J.Y. Wong , Yahya Almalki","doi":"10.1016/j.matcom.2025.10.028","DOIUrl":"10.1016/j.matcom.2025.10.028","url":null,"abstract":"<div><div>This study explores the nonlinear <span><math><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional double-chain deoxyribonucleic acid (DNA) model, which plays a central role in fundamental biological processes such as replication, transcription, and translation. Utilizing the <span><math><mrow><msup><mrow><mi>G</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>/</mo><mrow><mo>(</mo><mi>b</mi><msup><mrow><mi>G</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>+</mo><mi>G</mi><mo>+</mo><mi>a</mi><mo>)</mo></mrow></mrow></math></span>-expansion method, we derive new exact solutions in the domain of hyperbolic and trigonometric functions. Various soliton structures, such as kink, singular, and singular periodic solitons, are constructed and illustrated through 3D, density, and 2D profiles by means of suitable parameter choices. A qualitative analysis is carried out using the concepts of bifurcation and chaos theory to gain deeper insights. A parameter-dependent bifurcation analysis reveals how minute alterations in parameters can instigate significant fluctuations in system stability. More specifically, a perturbation term is introduced to investigate chaotic responses, which are verified by different detecting tools, Kaplan–Yorke dimension and multistability. To further emphasize the dynamic nature of the model, sensitivity analysis is performed under three distinct initial conditions. These findings expand our understanding of the nonlinear nature of DNA systems and provide fresh perspectives on their stability and complexity.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 527-541"},"PeriodicalIF":4.4,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-22DOI: 10.1016/j.matcom.2025.10.029
Sheng Su, Junxiang Yang
Binary image segmentation is a fundamental task in image analysis, often requiring methods that ensure both stability and interface continuity. In this paper, inspired by the Allen–Cahn equation, we propose a semi-analytical penalized threshold dynamics method to improve the efficiency and stability of binary image segmentation. The method employs a spectral approach in conjunction with operator splitting techniques to effectively address different components of the problem. First, the penalization term is solved analytically, allowing for accurate treatment of intensity differences. Next, the spectral method is utilized to solve the heat equation, providing exact solutions for the dynamics of interface evolution. Finally, a thresholding step is applied to achieve a clear demarcation of the interface. It is shown that the maximum principle is preserved throughout the whole process. The method can also be extended to three-dimensional (3D) segmentation, allowing for the analysis of volumetric data. This framework provides a robust approach to stable segmentation, preserving interface continuity and accurate region differentiation in both 2D and 3D contexts. Visual results demonstrate the effectiveness of the method across various image segmentation tasks, highlighting its potential for practical applications in binary image analysis. The basic 2D code implementation is provided in the appendix for reproducibility and further exploration.
{"title":"Semi-analytical penalized threshold dynamics method for binary image segmentation","authors":"Sheng Su, Junxiang Yang","doi":"10.1016/j.matcom.2025.10.029","DOIUrl":"10.1016/j.matcom.2025.10.029","url":null,"abstract":"<div><div>Binary image segmentation is a fundamental task in image analysis, often requiring methods that ensure both stability and interface continuity. In this paper, inspired by the Allen–Cahn equation, we propose a semi-analytical penalized threshold dynamics method to improve the efficiency and stability of binary image segmentation. The method employs a spectral approach in conjunction with operator splitting techniques to effectively address different components of the problem. First, the penalization term is solved analytically, allowing for accurate treatment of intensity differences. Next, the spectral method is utilized to solve the heat equation, providing exact solutions for the dynamics of interface evolution. Finally, a thresholding step is applied to achieve a clear demarcation of the interface. It is shown that the maximum principle is preserved throughout the whole process. The method can also be extended to three-dimensional (3D) segmentation, allowing for the analysis of volumetric data. This framework provides a robust approach to stable segmentation, preserving interface continuity and accurate region differentiation in both 2D and 3D contexts. Visual results demonstrate the effectiveness of the method across various image segmentation tasks, highlighting its potential for practical applications in binary image analysis. The basic 2D code implementation is provided in the appendix for reproducibility and further exploration.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 452-472"},"PeriodicalIF":4.4,"publicationDate":"2025-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-22DOI: 10.1016/j.matcom.2025.10.027
Chaoyue Guan , Jian Zhang
A high-order solver is presented for two-dimensional Riesz fractional nonlinear reaction–diffusion equations. It employs a midpoint starter and a three-point backward differentiation formula (BDF2) to achieve second-order temporal accuracy, together with a weighted Jacobi spectral approximation that delivers nearly exponential spatial convergence for analytic solutions. After Newton linearization, each correction is obtained via a penalized Levenberg–Marquardt minimum residual method (PLM-MRM). This iteration adaptively enforces boundary conditions without requiring boundary-fitted basis functions. We establish stability and rigorous a priori error bounds. Numerical experiments over a wide range of fractional orders confirm these rates and drive the residual to machine precision within a few PLM-MRM sweeps. Compared with a conventional LM update, global errors are reduced by up to 35%, and by one to two orders of magnitude relative to Galerkin-BDF or Crank–Nicolson (CN) baselines. For a given accuracy, the scheme allows time steps up to about four times larger than a recent fourth-order CN method.
{"title":"Adaptive spectral solver for Riesz fractional reaction–diffusion equations via penalized minimum residual iteration","authors":"Chaoyue Guan , Jian Zhang","doi":"10.1016/j.matcom.2025.10.027","DOIUrl":"10.1016/j.matcom.2025.10.027","url":null,"abstract":"<div><div>A high-order solver is presented for two-dimensional Riesz fractional nonlinear reaction–diffusion equations. It employs a midpoint starter and a three-point backward differentiation formula (BDF2) to achieve second-order temporal accuracy, together with a weighted Jacobi spectral approximation that delivers nearly exponential spatial convergence for analytic solutions. After Newton linearization, each correction is obtained via a penalized Levenberg–Marquardt minimum residual method (PLM-MRM). This iteration adaptively enforces boundary conditions without requiring boundary-fitted basis functions. We establish stability and rigorous a priori error bounds. Numerical experiments over a wide range of fractional orders confirm these rates and drive the residual to machine precision within a few PLM-MRM sweeps. Compared with a conventional LM update, global errors are reduced by up to 35%, and by one to two orders of magnitude relative to Galerkin-BDF or Crank–Nicolson (CN) baselines. For a given accuracy, the scheme allows time steps up to about four times larger than a recent fourth-order CN method.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 431-451"},"PeriodicalIF":4.4,"publicationDate":"2025-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-21DOI: 10.1016/j.matcom.2025.10.025
Kaiqian Yin, Yilin Chen, Xinzhu Meng
This paper considers a class of nonlocal vaccination epidemic models, where vaccination willingness decreases with increasing distance from the outbreak epicenter due to diminishing perception of the risk of contracting diseases. By establishing SVIR reaction–diffusion epidemic models with cognition, we continue to explore the application of Fick’s law and Fokker–Planck’s law in the diffusion of cognition. Meanwhile, we investigate the impact of different diffusion strategies adopted by vaccinated individuals on the final scale of nonlocal vaccination in spatially heterogeneous environment. Firstly, we conduct well-posedness analysis for both the random diffusion model and the symmetric diffusion model. We calculate the basic reproduction numbers of these models and conduct threshold dynamics analysis. Then, we obtain the corresponding degenerate model and prove the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium using the Lyapunov function. Finally, the results of numerical simulations demonstrate that different diffusion strategies and vaccination radii are associated with distinct spatial segregation phenomena. In the random diffusion model, if the diffusion strategy of vaccinated individuals is the same as that of susceptible individuals, the steady-state dispersion of vaccinated individuals closely resembles that of susceptible individuals. Conversely, if the diffusion strategy of vaccinated individuals is the same as that of infected individuals, they also demonstrate comparable equilibrium distributions. Intriguingly, this particular phenomenon failed to manifest in the remaining two model systems. Therefore, we speculate that Fokker–Planck’s law may better describe the human transmission patterns in infectious disease models.
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This paper explores the calculation of European option prices on energy futures using a time-varying volatility model enhanced by a regime switching factor. We develop a semi-analytical method to determine the price of European options on these energy futures, involving the derivation of the characteristic function for the energy futures’ dynamics. To determine the parameters of the regime switching model and identify when economic states change, we employ the EM algorithm, utilizing real gas futures price data. We validate our closed-form solution for the option pricing through simulations employing the generalized antithetic variates Monte-Carlo technique. A comprehensive numerical analysis demonstrates the effectiveness of our proposed methodology.
{"title":"Time-varying volatility model equipped with regime switching factor: Valuation of option price written on energy futures","authors":"Guillaume Leduc , Farshid Mehrdoust , Idin Noorani","doi":"10.1016/j.matcom.2025.10.023","DOIUrl":"10.1016/j.matcom.2025.10.023","url":null,"abstract":"<div><div>This paper explores the calculation of European option prices on energy futures using a time-varying volatility model enhanced by a regime switching factor. We develop a semi-analytical method to determine the price of European options on these energy futures, involving the derivation of the characteristic function for the energy futures’ dynamics. To determine the parameters of the regime switching model and identify when economic states change, we employ the EM algorithm, utilizing real gas futures price data. We validate our closed-form solution for the option pricing through simulations employing the generalized antithetic variates Monte-Carlo technique. A comprehensive numerical analysis demonstrates the effectiveness of our proposed methodology.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 844-867"},"PeriodicalIF":4.4,"publicationDate":"2025-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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