Pub Date : 2026-03-01Epub Date: 2025-10-08DOI: 10.1016/j.matcom.2025.10.009
Kexin Hua, Yawen Yan, Jimin Zhang
Various types of algae inhabit rivers/streams and they are susceptible to infection by lytic algae viruses. A Reaction–diffusion–advection model is developed to characterize lytic algae virus transmission in rivers/streams. Model dynamics are explored including the well-posedness of solutions, steady state solutions, and uniform persistence. We obtain two critical thresholds for algae survival and the spread of lytic algae viruses in rivers/streams. Numerical diagrams from the model illustrate that varying ecological factors influence lytic algae virus transmission and cause complex dynamics. Especially, lytic viruses have the capacity to reshape the spatial distribution of algae in rivers/streams and contribute to the regulation of algal blooms.
{"title":"A reaction–diffusion–advection model for lytic algae virus transmission in rivers/streams","authors":"Kexin Hua, Yawen Yan, Jimin Zhang","doi":"10.1016/j.matcom.2025.10.009","DOIUrl":"10.1016/j.matcom.2025.10.009","url":null,"abstract":"<div><div>Various types of algae inhabit rivers/streams and they are susceptible to infection by lytic algae viruses. A Reaction–diffusion–advection model is developed to characterize lytic algae virus transmission in rivers/streams. Model dynamics are explored including the well-posedness of solutions, steady state solutions, and uniform persistence. We obtain two critical thresholds for algae survival and the spread of lytic algae viruses in rivers/streams. Numerical diagrams from the model illustrate that varying ecological factors influence lytic algae virus transmission and cause complex dynamics. Especially, lytic viruses have the capacity to reshape the spatial distribution of algae in rivers/streams and contribute to the regulation of algal blooms.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 165-182"},"PeriodicalIF":4.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266135","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 : 2026-03-01Epub Date: 2025-08-25DOI: 10.1016/j.matcom.2025.08.018
Xinyu Diao, Bo Yu, Haitao Qi
This article provides uniform and efficient numerical approaches for the generalized two-dimensional Oldroyd-B type multi-term fractional mixed diffusion and diffusion-wave model. Firstly, a compact alternating direction implicit (ADI) method is proposed with convergence accuracy , where , and are orders of the fractional derivatives, , and are the time and space step sizes, respectively. The convergence analysis of the proposed compact ADI method is investigated strictly utilizing the energy estimation technique. Secondly, in order to improve the accuracy in the temporal direction, an improved compact ADI method with convergence accuracy is constructed, the convergence analysis is also clarified using the energy estimation method. Lastly, the proposed compact ADI methods are implemented on MATLAB platform. The numerical simulation results are listed in tabular forms, which manifest the validity of the derived numerical methods.
{"title":"Compact ADI methods for the generalized two-dimensional Oldroyd-B type multi-term fractional mixed diffusion and diffusion-wave model","authors":"Xinyu Diao, Bo Yu, Haitao Qi","doi":"10.1016/j.matcom.2025.08.018","DOIUrl":"10.1016/j.matcom.2025.08.018","url":null,"abstract":"<div><div>This article provides uniform and efficient numerical approaches for the generalized two-dimensional Oldroyd-B type multi-term fractional mixed diffusion and diffusion-wave model. Firstly, a compact alternating direction implicit (ADI) method is proposed with convergence accuracy <span><math><mrow><mi>O</mi><mfenced><mrow><msup><mrow><mi>τ</mi></mrow><mrow><mo>min</mo><mfenced><mrow><mn>3</mn><mo>−</mo><msub><mrow><mi>γ</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>,</mo><mn>2</mn><mo>−</mo><msub><mrow><mi>β</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>,</mo><mn>2</mn><mo>−</mo><mi>α</mi><mo>,</mo><mn>1</mn><mo>+</mo><msub><mrow><mi>γ</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>−</mo><mn>2</mn><mi>α</mi></mrow></mfenced></mrow></msup><mo>+</mo><msubsup><mrow><mi>h</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>h</mi></mrow><mrow><mi>y</mi></mrow><mrow><mn>4</mn></mrow></msubsup></mrow></mfenced></mrow></math></span>, where <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>l</mi></mrow></msub></math></span>, <span><math><msub><mrow><mi>β</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span> and <span><math><mi>α</mi></math></span> are orders of the fractional derivatives, <span><math><mi>τ</mi></math></span>, <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>y</mi></mrow></msub></math></span> are the time and space step sizes, respectively. The convergence analysis of the proposed compact ADI method is investigated strictly utilizing the energy estimation technique. Secondly, in order to improve the accuracy in the temporal direction, an improved compact ADI method with convergence accuracy <span><math><mrow><mi>O</mi><mfenced><mrow><msup><mrow><mi>τ</mi></mrow><mrow><mo>min</mo><mfenced><mrow><mn>3</mn><mo>−</mo><msub><mrow><mi>γ</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>,</mo><mn>2</mn><mo>−</mo><msub><mrow><mi>β</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>,</mo><mn>2</mn><mo>−</mo><mi>α</mi></mrow></mfenced></mrow></msup><mo>+</mo><msubsup><mrow><mi>h</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>h</mi></mrow><mrow><mi>y</mi></mrow><mrow><mn>4</mn></mrow></msubsup></mrow></mfenced></mrow></math></span> is constructed, the convergence analysis is also clarified using the energy estimation method. Lastly, the proposed compact ADI methods are implemented on MATLAB platform. The numerical simulation results are listed in tabular forms, which manifest the validity of the derived numerical methods.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 281-299"},"PeriodicalIF":4.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020073","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 : 2026-03-01Epub Date: 2025-10-20DOI: 10.1016/j.matcom.2025.10.016
Huixian Wang, Yan Qiao, Hua Wu
This paper proposes an efficient space–time spectral method for solving the parameter identification problem of two-dimensional heat conduction equations. The spatial discretization employs the Legendre–Galerkin spectral method, while the temporal direction utilizes the Legendre-tau spectral method. Optimal error estimates of the semi-discrete scheme are established in the -norm. For the large-scale matrix systems generated by high-dimensional discretization, tensor product matrix decomposition coupled with sparse preconditioning is adopted. The proposed algorithm is implemented by using an implicit–explicit iterative scheme, where the nonlinear terms are efficiently computed through the fast Legendre transform. Additionally, a multi-interval spectral method in time is utilized to overcome the computational difficulties associated with long-time simulations. For noise perturbations, we also investigate the stability performance of the space–time spectral scheme. Numerical experiments demonstrate the efficiency, stability, and robustness of the proposed algorithm.
{"title":"A high-order stable method for unknown parameter identification in the 2D heat conduction equation","authors":"Huixian Wang, Yan Qiao, Hua Wu","doi":"10.1016/j.matcom.2025.10.016","DOIUrl":"10.1016/j.matcom.2025.10.016","url":null,"abstract":"<div><div>This paper proposes an efficient space–time spectral method for solving the parameter identification problem of two-dimensional heat conduction equations. The spatial discretization employs the Legendre–Galerkin spectral method, while the temporal direction utilizes the Legendre-tau spectral method. Optimal error estimates of the semi-discrete scheme are established in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm. For the large-scale matrix systems generated by high-dimensional discretization, tensor product matrix decomposition coupled with sparse preconditioning is adopted. The proposed algorithm is implemented by using an implicit–explicit iterative scheme, where the nonlinear terms are efficiently computed through the fast Legendre transform. Additionally, a multi-interval spectral method in time is utilized to overcome the computational difficulties associated with long-time simulations. For noise perturbations, we also investigate the stability performance of the space–time spectral scheme. Numerical experiments demonstrate the efficiency, stability, and robustness of the proposed algorithm.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 825-843"},"PeriodicalIF":4.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362632","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 : 2026-03-01Epub Date: 2025-10-16DOI: 10.1016/j.matcom.2025.10.010
A. Dòria-Cerezo, M. Velasco, I. Zaplana, P. Martí
This paper introduces the modelling of three-phase electrical systems using the Geometric Algebra approach and is compared with the complex-valued framework in the case of non-symmetrical conditions. The main benefit of the geometric algebra framework is the possibility of representing the dynamics of unbalanced scenarios by a single-input, single-output relationship. The paper presents step-by-step, building the geometric impedance and revisiting Ohm’s law, and compares the complex-valued modelling widely used in balanced three-phase circuits.
{"title":"The Ohm’s Law for (non-symmetric) three-phase three-wire electrical circuits: From a complex-valued to a geometric algebra approach","authors":"A. Dòria-Cerezo, M. Velasco, I. Zaplana, P. Martí","doi":"10.1016/j.matcom.2025.10.010","DOIUrl":"10.1016/j.matcom.2025.10.010","url":null,"abstract":"<div><div>This paper introduces the modelling of three-phase electrical systems using the Geometric Algebra approach and is compared with the complex-valued framework in the case of non-symmetrical conditions. The main benefit of the geometric algebra framework is the possibility of representing the dynamics of unbalanced scenarios by a single-input, single-output relationship. The paper presents step-by-step, building the <em>geometric impedance</em> and revisiting Ohm’s law, and compares the complex-valued modelling widely used in balanced three-phase circuits.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 473-488"},"PeriodicalIF":4.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362750","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 : 2026-03-01Epub Date: 2025-09-17DOI: 10.1016/j.matcom.2025.09.010
Tarun Mohan , Hana M. Dobrovolny
SARS-CoV-2 has become an endemic virus that is partly kept in check by annual vaccination. A number of different vaccines are available to prevent severe illness from SARS-CoV-2 infection. These vaccines are based on different vaccine modalities and have the potential to elicit slightly different immune responses. Unfortunately, more recent strains of SARS-CoV-2 appear to have the ability to evade some of the immune protection provided by vaccines. While the genesis for the large number of vaccines was the need to rapidly develop a vaccine that was effective against SARS-CoV-2, researchers have speculated that having multiple vaccines with different mechanisms would make it harder for the virus to mutate enough to evade all the vaccines. In this manuscript, we use mathematical models to determine whether use of multiple vaccines decreases the likelihood of evolving a virus strain that can evade all the vaccines. We use a series of models, ranging from one to three vaccines, to measure the fraction of fully escaped virus infections during an epidemic. We find that vaccination rates need to be higher (higher vaccine pressure) in order for a virus to escape all vaccines as the number of vaccines increases. This suggests that the use of multiple vaccines has a population-wide protective effect since this makes it more difficult for the virus to fully escape all vaccines.
{"title":"Mathematical modeling of the effect of multiple vaccines on viral escape","authors":"Tarun Mohan , Hana M. Dobrovolny","doi":"10.1016/j.matcom.2025.09.010","DOIUrl":"10.1016/j.matcom.2025.09.010","url":null,"abstract":"<div><div>SARS-CoV-2 has become an endemic virus that is partly kept in check by annual vaccination. A number of different vaccines are available to prevent severe illness from SARS-CoV-2 infection. These vaccines are based on different vaccine modalities and have the potential to elicit slightly different immune responses. Unfortunately, more recent strains of SARS-CoV-2 appear to have the ability to evade some of the immune protection provided by vaccines. While the genesis for the large number of vaccines was the need to rapidly develop a vaccine that was effective against SARS-CoV-2, researchers have speculated that having multiple vaccines with different mechanisms would make it harder for the virus to mutate enough to evade all the vaccines. In this manuscript, we use mathematical models to determine whether use of multiple vaccines decreases the likelihood of evolving a virus strain that can evade all the vaccines. We use a series of models, ranging from one to three vaccines, to measure the fraction of fully escaped virus infections during an epidemic. We find that vaccination rates need to be higher (higher vaccine pressure) in order for a virus to escape all vaccines as the number of vaccines increases. This suggests that the use of multiple vaccines has a population-wide protective effect since this makes it more difficult for the virus to fully escape all vaccines.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 408-429"},"PeriodicalIF":4.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106066","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 : 2026-03-01Epub Date: 2025-11-06DOI: 10.1016/j.matcom.2025.11.003
Yanxia Zhang , Xiaolin Li
In this paper, an element-free Galerkin (EFG) method is proposed for solving delay-reaction–diffusion (DRD) equations. A fully discrete EFG system is developed by integrating a second-order time discretization with a penalized EFG spatial discretization. The unconditional stability of the time semi-discrete system is analyzed, and then the theoretical error of the meshless fully discrete system is derived. Finally, through numerical experiments, the validity of the method is verified and the theoretical result is confirmed.
{"title":"An element-free Galerkin method for linear and nonlinear delay-reaction-diffusion equations","authors":"Yanxia Zhang , Xiaolin Li","doi":"10.1016/j.matcom.2025.11.003","DOIUrl":"10.1016/j.matcom.2025.11.003","url":null,"abstract":"<div><div>In this paper, an element-free Galerkin (EFG) method is proposed for solving delay-reaction–diffusion (DRD) equations. A fully discrete EFG system is developed by integrating a second-order time discretization with a penalized EFG spatial discretization. The unconditional stability of the time semi-discrete system is analyzed, and then the theoretical error of the meshless fully discrete system is derived. Finally, through numerical experiments, the validity of the method is verified and the theoretical result is confirmed.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 707-723"},"PeriodicalIF":4.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145519954","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 : 2026-03-01Epub Date: 2025-09-17DOI: 10.1016/j.matcom.2025.09.011
Ping Yang , Yiping Lin
In this paper, a two-dimensional complex network with delayed feedback control is proposed and discussed. For the network without control, the equilibrium of the network is unstable, but under the control with even very small parameters, the equilibrium of the network will become stable. A detailed stability analysis on the controlled system is provided. Differing from the previous works, on the coordinate plane of two delays, the stability region is surrounded by the critical curves. The supercritical and the subcritical Hopf bifurcations are discussed particularly along the boundary of the stability region. Numerical simulations are provided to illustrate the results. The investigation shows that there is stable region surrounded by five critical curves and there exist doubling-periodic solutions and chaotic solutions in the controlled network when the parameters keep away from the stability region. This work provides a theoretical basis for the further application of complex networks.
{"title":"Critical curves and stability region in a complex network with delayed feedback control","authors":"Ping Yang , Yiping Lin","doi":"10.1016/j.matcom.2025.09.011","DOIUrl":"10.1016/j.matcom.2025.09.011","url":null,"abstract":"<div><div>In this paper, a two-dimensional complex network with delayed feedback control is proposed and discussed. For the network without control, the equilibrium of the network is unstable, but under the control with even very small parameters, the equilibrium of the network will become stable. A detailed stability analysis on the controlled system is provided. Differing from the previous works, on the coordinate plane of two delays, the stability region is surrounded by the critical curves. The supercritical and the subcritical Hopf bifurcations are discussed particularly along the boundary of the stability region. Numerical simulations are provided to illustrate the results. The investigation shows that there is stable region surrounded by five critical curves and there exist doubling-periodic solutions and chaotic solutions in the controlled network when the parameters keep away from the stability region. This work provides a theoretical basis for the further application of complex networks.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 548-561"},"PeriodicalIF":4.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158541","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 : 2026-03-01Epub Date: 2025-08-26DOI: 10.1016/j.matcom.2025.08.002
Mengqing Jin , Xinlong Feng , Kun Wang
In this paper, we study unconditional structure preserving fully discrete finite element method (FEM) for the Keller–Segel equations on closed surfaces. Based on the equivalent form got from the Slotboom transformation, applying the surface finite element method (SFEM) and the Euler scheme in space and time, we present a fully discrete scheme for the Keller–Segel equations. Then, by modifying the approximation of the exponential function with piecewise local geometric means and introducing two auxiliary variables with respect to the Slotboom transformation to split the coupling, and applying the lump process to the mass matrix, we get a new structure preserving fully discrete finite element scheme. The proposed scheme is rigorously proved to be stable, unconditionally mass conservative, positivity preserving and energy dissipative. Moreover, at each time step, only the linear elliptic equation with constant coefficient needs to be solved, which can be implemented efficiently. Finally, a number of numerical experiments are shown to demonstrate the theoretical analysis.
{"title":"Unconditional structure preserving fully discrete finite element method for the Keller–Segel equations on closed surfaces","authors":"Mengqing Jin , Xinlong Feng , Kun Wang","doi":"10.1016/j.matcom.2025.08.002","DOIUrl":"10.1016/j.matcom.2025.08.002","url":null,"abstract":"<div><div>In this paper, we study unconditional structure preserving fully discrete finite element method (FEM) for the Keller–Segel equations on closed surfaces. Based on the equivalent form got from the Slotboom transformation, applying the surface finite element method (SFEM) and the Euler scheme in space and time, we present a fully discrete scheme for the Keller–Segel equations. Then, by modifying the approximation of the exponential function with piecewise local geometric means and introducing two auxiliary variables with respect to the Slotboom transformation to split the coupling, and applying the lump process to the mass matrix, we get a new structure preserving fully discrete finite element scheme. The proposed scheme is rigorously proved to be stable, unconditionally mass conservative, positivity preserving and energy dissipative. Moreover, at each time step, only the linear elliptic equation with constant coefficient needs to be solved, which can be implemented efficiently. Finally, a number of numerical experiments are shown to demonstrate the theoretical analysis.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 171-189"},"PeriodicalIF":4.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144926131","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 : 2026-03-01Epub Date: 2025-10-11DOI: 10.1016/j.matcom.2025.10.012
Lei Cui , Qiong-Ao Huang , Gengen Zhang
This work presents a mathematical framework to develop energy-preserving, high-order linearly implicit Runge–Kutta (RK) methods for general Hamiltonian PDEs. This reformulation results in a two-stage second-order IMEX-RK method that is unconditionally energy-stable, with its diagonally implicit part satisfying the symplectic condition. In contrast, the search for a third-order IMEX-RK scheme that similarly guarantees unconditional energy-stable has been unsuccessful. To achieve a higher-order energy-preserving scheme, we incorporate a relaxation factor into the conventional IMEX-RK method, leading to the development of a class of high-order relaxed IMEX-RK (RIMEX-RK) methods. A rigorous theoretical analysis demonstrates the derived methods’ energy stability and error convergence. Key advantages of the RIMEX-RK methods include their one-step nature, high-order accuracy, energy preservation, and ease of implementation. Extensive numerical experiments demonstrate the framework’s superior performance.
{"title":"High-order and energy-preserving relaxed implicit–explicit Runge–Kutta methods for Hamiltonian PDEs","authors":"Lei Cui , Qiong-Ao Huang , Gengen Zhang","doi":"10.1016/j.matcom.2025.10.012","DOIUrl":"10.1016/j.matcom.2025.10.012","url":null,"abstract":"<div><div>This work presents a mathematical framework to develop energy-preserving, high-order linearly implicit Runge–Kutta (RK) methods for general Hamiltonian PDEs. This reformulation results in a two-stage second-order IMEX-RK method that is unconditionally energy-stable, with its diagonally implicit part satisfying the symplectic condition. In contrast, the search for a third-order IMEX-RK scheme that similarly guarantees unconditional energy-stable has been unsuccessful. To achieve a higher-order energy-preserving scheme, we incorporate a relaxation factor into the conventional IMEX-RK method, leading to the development of a class of high-order relaxed IMEX-RK (RIMEX-RK) methods. A rigorous theoretical analysis demonstrates the derived methods’ energy stability and error convergence. Key advantages of the RIMEX-RK methods include their one-step nature, high-order accuracy, energy preservation, and ease of implementation. Extensive numerical experiments demonstrate the framework’s superior performance.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 205-224"},"PeriodicalIF":4.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145320479","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 : 2026-03-01Epub Date: 2025-10-13DOI: 10.1016/j.matcom.2025.08.029
Allal El Moubarek Bouzid , Corinne Alonso , Gerard Beral
This study investigates the effectiveness of hybrid power-sharing control strategies in microgrid systems. It integrates various droop controllers, including conventional droop, universal droop, dVOC, and VSG. The contribution of each controller is evaluated in terms of system stability, efficiency, and adaptability. These assessments consider how different test conditions influence overall system performance. The performance analysis focuses on power sharing during both transient and steady-state conditions. It accounts for DERs connected through complex transmission line impedances and subjected to variable local loads. The study concludes with extensive real-time simulations using the Typhoon HIL 604 platform. These scenarios test different operating conditions to identify the most stable microgrid configuration.
{"title":"Challenges of operating multiple distributed generators with different primary control strategies in microgrids: Interactions and performance assessment","authors":"Allal El Moubarek Bouzid , Corinne Alonso , Gerard Beral","doi":"10.1016/j.matcom.2025.08.029","DOIUrl":"10.1016/j.matcom.2025.08.029","url":null,"abstract":"<div><div>This study investigates the effectiveness of hybrid power-sharing control strategies in microgrid systems. It integrates various droop controllers, including conventional droop, universal droop, dVOC, and VSG. The contribution of each controller is evaluated in terms of system stability, efficiency, and adaptability. These assessments consider how different test conditions influence overall system performance. The performance analysis focuses on power sharing during both transient and steady-state conditions. It accounts for DERs connected through complex transmission line impedances and subjected to variable local loads. The study concludes with extensive real-time simulations using the Typhoon HIL 604 platform. These scenarios test different operating conditions to identify the most stable microgrid configuration.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 312-334"},"PeriodicalIF":4.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145320483","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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