Pub Date : 2026-05-01Epub Date: 2026-01-05DOI: 10.1016/S0378-4754(25)00563-4
{"title":"IMACS Calendar of Events","authors":"","doi":"10.1016/S0378-4754(25)00563-4","DOIUrl":"10.1016/S0378-4754(25)00563-4","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"243 ","pages":"Page 525"},"PeriodicalIF":4.4,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145924836","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 : 2026-05-01Epub Date: 2025-11-30DOI: 10.1016/j.matcom.2025.11.038
Huanyi Wang, Suxia Zhang, Jinhu Xu, Xingyu Zhang
During an epidemic outbreak, the release of contagion data and related information in media coverage enhances protective awareness among individuals, thereby prompting behavioral adaptations that subsequently influence disease transmission dynamics. To explore the feedback mechanism between the dynamics of epidemic progression and social media, an SIR-M model incorporating the hierarchical impact of media-induced awareness is established, characterizing the distinct levels of behavioral response based on the perception of potential risks within the population. The analysis and application of the proposed model are conducted extensively and comprehensively. The findings demonstrate that under specific parametric conditions, the decay rate of media coverage can destabilize the endemic equilibrium and induce a Hopf bifurcation. This phenomenon is further confirmed by both one- and two-parameter bifurcation diagrams. Using particle swarm optimization algorithm for parameter estimation, we show that the proposed model effectively captures the temporal trends of both COVID-19 case data and related media coverage, revealing the hierarchical nature of protection awareness.
{"title":"Hierarchical impact of media-induced awareness on epidemic dynamics: Analysis and application of an SIR-M model","authors":"Huanyi Wang, Suxia Zhang, Jinhu Xu, Xingyu Zhang","doi":"10.1016/j.matcom.2025.11.038","DOIUrl":"10.1016/j.matcom.2025.11.038","url":null,"abstract":"<div><div>During an epidemic outbreak, the release of contagion data and related information in media coverage enhances protective awareness among individuals, thereby prompting behavioral adaptations that subsequently influence disease transmission dynamics. To explore the feedback mechanism between the dynamics of epidemic progression and social media, an SIR-M model incorporating the hierarchical impact of media-induced awareness is established, characterizing the distinct levels of behavioral response based on the perception of potential risks within the population. The analysis and application of the proposed model are conducted extensively and comprehensively. The findings demonstrate that under specific parametric conditions, the decay rate of media coverage can destabilize the endemic equilibrium and induce a Hopf bifurcation. This phenomenon is further confirmed by both one- and two-parameter bifurcation diagrams. Using particle swarm optimization algorithm for parameter estimation, we show that the proposed model effectively captures the temporal trends of both COVID-19 case data and related media coverage, revealing the hierarchical nature of protection awareness.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"243 ","pages":"Pages 307-326"},"PeriodicalIF":4.4,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685315","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 : 2026-05-01Epub Date: 2025-11-21DOI: 10.1016/j.matcom.2025.11.022
Mohammad Amini , Ramin Vatankhah , Mohammad Mehdi Arefi
Recent advancements in mathematical modeling have enhanced the analysis of cancer responses to treatments, particularly in the promising field of chemovirotherapy. The present research introduces a novel data-driven mathematical model of chemovirotherapy that comprehensively incorporates the immune response. This thorough consideration of the immune system enables a comparative analysis of chemovirotherapy with immunotherapy, specifically CD8+T cells, CD4+T cells, and IL-2 cytokine therapies. By estimating a Michaelis-Menten constant from empirical therapy data for virotherapy, the computational efficiency of the dynamical system is enhanced while maintaining high accuracy in capturing virotherapy dynamics. Parameters are estimated using the Unscented Kalman Filter based on data from human melanoma cell lines. A stability analysis investigates parameter-dependent equilibrium shifts of the model, revealing that treatments such as chemotherapy destabilize the system at any dosage, which may inform treatment scenarios. Numerical simulations conducted on the model demonstrate that the combination of chemotherapy and virotherapy yields superior outcomes, particularly in cases of high tumor burden and weakened immune systems. This study presents a comprehensive framework for comparing immunotherapy, chemotherapy, and virotherapy, thereby advancing cancer therapeutic modeling and facilitating the optimization of comparative treatment strategies.
{"title":"Enhancing chemovirotherapy through a data-driven model with detailed consideration of immune system response using Unscented Kalman Filter","authors":"Mohammad Amini , Ramin Vatankhah , Mohammad Mehdi Arefi","doi":"10.1016/j.matcom.2025.11.022","DOIUrl":"10.1016/j.matcom.2025.11.022","url":null,"abstract":"<div><div>Recent advancements in mathematical modeling have enhanced the analysis of cancer responses to treatments, particularly in the promising field of chemovirotherapy. The present research introduces a novel data-driven mathematical model of chemovirotherapy that comprehensively incorporates the immune response. This thorough consideration of the immune system enables a comparative analysis of chemovirotherapy with immunotherapy, specifically CD8<sup>+</sup>T cells, CD4<sup>+</sup>T cells, and IL-2 cytokine therapies. By estimating a Michaelis-Menten constant from empirical therapy data for virotherapy, the computational efficiency of the dynamical system is enhanced while maintaining high accuracy in capturing virotherapy dynamics. Parameters are estimated using the Unscented Kalman Filter based on data from human melanoma cell lines. A stability analysis investigates parameter-dependent equilibrium shifts of the model, revealing that treatments such as chemotherapy destabilize the system at any dosage, which may inform treatment scenarios. Numerical simulations conducted on the model demonstrate that the combination of chemotherapy and virotherapy yields superior outcomes, particularly in cases of high tumor burden and weakened immune systems. This study presents a comprehensive framework for comparing immunotherapy, chemotherapy, and virotherapy, thereby advancing cancer therapeutic modeling and facilitating the optimization of comparative treatment strategies.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"243 ","pages":"Pages 283-306"},"PeriodicalIF":4.4,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685416","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 : 2026-05-01Epub Date: 2025-11-19DOI: 10.1016/j.matcom.2025.11.019
Miao Chen , Shijie Zhao , Tianran Zhang , Xin Yu
Constrained multi-objective optimization problems (CMOPs) constitute a prevalent and ubiquitous class of optimization challenges that are frequently encountered across diverse field within science and engineering. To solve the complementary multi-objective optimization problem with narrow and disconnected feasible regions, dual-population two-archive evolutionary framework for constrained multi-objective optimization with constrained-archive solution phase-transition and auxiliary-population environment selection pause-termination (CAE_2SP) is proposed. The algorithm uses dual-population with different efficacy and two archives with different functions. To improve the problem of lower population diversity, constrained-archive solution phase-transition strategy is proposed. In this strategy, the diversity of solutions is emphasized in the early generation, so the non-dominated infeasible solutions generated by the evolution of main population are stored in the archive. In the late generation, the feasibility of solutions is taken into account, hence, constrained archive is transformed into storing non-dominated feasible solutions. In addition, this paper puts forward auxiliary-population environment selection pause-termination strategy. In this strategy, auxiliary population stop updating in the late generation and uses the optimal population information in the early generation to guide the evolution, to reduce the consumption of computing resources in the late generation and provide more computing resources for main population to help it search for potential feasible regions. The experimental results of nine comparison algorithms in three benchmark function suites demonstrate that CAE_2SP has superior performance in solving CMOPs compared with others. To validate the applicability of the proposed algorithm in solving practical problems, six real-world problems are employed for testing. The experimental results demonstrate that CAE_2SP exhibits competitive performance in addressing practical issues.
{"title":"Dual-population two-archive evolutionary framework for constrained multi-objective optimization","authors":"Miao Chen , Shijie Zhao , Tianran Zhang , Xin Yu","doi":"10.1016/j.matcom.2025.11.019","DOIUrl":"10.1016/j.matcom.2025.11.019","url":null,"abstract":"<div><div>Constrained multi-objective optimization problems (CMOPs) constitute a prevalent and ubiquitous class of optimization challenges that are frequently encountered across diverse field within science and engineering. To solve the complementary multi-objective optimization problem with narrow and disconnected feasible regions, dual-population two-archive evolutionary framework for constrained multi-objective optimization with constrained-archive solution phase-transition and auxiliary-population environment selection pause-termination (CAE_2SP) is proposed. The algorithm uses dual-population with different efficacy and two archives with different functions. To improve the problem of lower population diversity, constrained-archive solution phase-transition strategy is proposed. In this strategy, the diversity of solutions is emphasized in the early generation, so the non-dominated infeasible solutions generated by the evolution of main population are stored in the archive. In the late generation, the feasibility of solutions is taken into account, hence, constrained archive is transformed into storing non-dominated feasible solutions. In addition, this paper puts forward auxiliary-population environment selection pause-termination strategy. In this strategy, auxiliary population stop updating in the late generation and uses the optimal population information in the early generation to guide the evolution, to reduce the consumption of computing resources in the late generation and provide more computing resources for main population to help it search for potential feasible regions. The experimental results of nine comparison algorithms in three benchmark function suites demonstrate that CAE_2SP has superior performance in solving CMOPs compared with others. To validate the applicability of the proposed algorithm in solving practical problems, six real-world problems are employed for testing. The experimental results demonstrate that CAE_2SP exhibits competitive performance in addressing practical issues.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"243 ","pages":"Pages 196-220"},"PeriodicalIF":4.4,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145618556","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 : 2026-05-01Epub Date: 2026-01-05DOI: 10.1016/S0378-4754(25)00562-2
{"title":"News of IMACS","authors":"","doi":"10.1016/S0378-4754(25)00562-2","DOIUrl":"10.1016/S0378-4754(25)00562-2","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"243 ","pages":"Page 524"},"PeriodicalIF":4.4,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145924835","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 : 2026-05-01Epub Date: 2025-11-22DOI: 10.1016/j.matcom.2025.11.027
Yi Zhang , Jin Song , Wenjie Zuo , Zhengdi Zhang
This paper aims to explore compound relaxation oscillations and underlying mechanisms in the dynamical system with periodic non-smoothness, focusing on the effect of non-smooth bifurcations on compound relaxation oscillations. Based on the Rayleigh–Duffing system with external excitation, a modified non-smooth dynamical system is developed by introducing a periodic term that represents discontinuous external influences, such as wave-induced forces in ship rolling dynamics. Various non-smooth bifurcation phenomena are systematically investigated, including non-smooth homoclinic bifurcation, C-bifurcation, persistence bifurcation, and non-smooth fold bifurcation. Five different oscillation modes are demonstrated through numerical simulations, and their mechanisms are revealed in combination with the slow–fast analysis. It is found that the non-smooth homoclinic bifurcation significantly alters the oscillation process and induces transitions between stable states. The C-bifurcation has less effect on the oscillation mode even though it changes the topology of limit cycles. Different types of boundary equilibrium bifurcations lead to substantial changes in the stability and structure of compound relaxation oscillations. In addition, two types of coexisting attractors are identified through the basin of attraction, indicating multistability that gives rise to different oscillation modes.
{"title":"Compound relaxation oscillations in a modified Rayleigh–Duffing system with periodic non-smoothness","authors":"Yi Zhang , Jin Song , Wenjie Zuo , Zhengdi Zhang","doi":"10.1016/j.matcom.2025.11.027","DOIUrl":"10.1016/j.matcom.2025.11.027","url":null,"abstract":"<div><div>This paper aims to explore compound relaxation oscillations and underlying mechanisms in the dynamical system with periodic non-smoothness, focusing on the effect of non-smooth bifurcations on compound relaxation oscillations. Based on the Rayleigh–Duffing system with external excitation, a modified non-smooth dynamical system is developed by introducing a periodic term that represents discontinuous external influences, such as wave-induced forces in ship rolling dynamics. Various non-smooth bifurcation phenomena are systematically investigated, including non-smooth homoclinic bifurcation, C-bifurcation, persistence bifurcation, and non-smooth fold bifurcation. Five different oscillation modes are demonstrated through numerical simulations, and their mechanisms are revealed in combination with the slow–fast analysis. It is found that the non-smooth homoclinic bifurcation significantly alters the oscillation process and induces transitions between stable states. The C-bifurcation has less effect on the oscillation mode even though it changes the topology of limit cycles. Different types of boundary equilibrium bifurcations lead to substantial changes in the stability and structure of compound relaxation oscillations. In addition, two types of coexisting attractors are identified through the basin of attraction, indicating multistability that gives rise to different oscillation modes.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"243 ","pages":"Pages 82-94"},"PeriodicalIF":4.4,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145618555","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 : 2026-05-01Epub Date: 2025-12-01DOI: 10.1016/j.matcom.2025.11.040
Priyanka Harjule , Harshit , Rajesh Kumar
Dengue fever is a major viral disease that spreads through mosquitoes and is a public health concern, especially in some tropical and subtropical regions. Traditional integer-order compartmental models often do not work well at modeling how disease spreads over time, which is often affected by past infection rates and environmental factors. We propose a hybrid SEISRD-SI model that combines integer-order and fractional-order dynamics with the Caputo derivative. It also includes compartments for severe dengue and dengue-induced mortality to better represent how the disease spreads and what happens as a result. The existence and uniqueness of the fractional model are proved using the Banach Fixed Point Theorem. The basic reproduction number is derived using the next generation matrix method, which provides key insights into disease spread thresholds. The hybrid model is calibrated using weekly dengue incidence data from Brazil, and parameters are optimized through Particle Swarm Optimization. The optimized hybrid model lowers the mean relative error (MRE) by up to 6.12% compared to the Caputo fractional-order model (MRE: 20.90%) and the integer-order model (MRE: 24.15%). These findings highlight the ability of hybrid modeling to capture both peak and non-peak epidemic dynamics and underscore the value of fractional calculus in advancing epidemiological modeling frameworks.
{"title":"A hybrid integer-Caputo fractional order dengue transmission model: Parameter optimization and empirical study with real-world data","authors":"Priyanka Harjule , Harshit , Rajesh Kumar","doi":"10.1016/j.matcom.2025.11.040","DOIUrl":"10.1016/j.matcom.2025.11.040","url":null,"abstract":"<div><div>Dengue fever is a major viral disease that spreads through mosquitoes and is a public health concern, especially in some tropical and subtropical regions. Traditional integer-order compartmental models often do not work well at modeling how disease spreads over time, which is often affected by past infection rates and environmental factors. We propose a hybrid SEISRD-SI model that combines integer-order and fractional-order dynamics with the Caputo derivative. It also includes compartments for severe dengue and dengue-induced mortality to better represent how the disease spreads and what happens as a result. The existence and uniqueness of the fractional model are proved using the Banach Fixed Point Theorem. The basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is derived using the next generation matrix method, which provides key insights into disease spread thresholds. The hybrid model is calibrated using weekly dengue incidence data from Brazil, and parameters are optimized through Particle Swarm Optimization. The optimized hybrid model lowers the mean relative error (MRE) by up to 6.12% compared to the Caputo fractional-order model (MRE: 20.90%) and the integer-order model (MRE: 24.15%). These findings highlight the ability of hybrid modeling to capture both peak and non-peak epidemic dynamics and underscore the value of fractional calculus in advancing epidemiological modeling frameworks.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"243 ","pages":"Pages 339-361"},"PeriodicalIF":4.4,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685316","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 : 2026-05-01Epub Date: 2025-12-11DOI: 10.1016/j.matcom.2025.12.005
A. El-Mesady , M.A. Abdelkawy , Muhammad Farhan , Mohammad Izadi
This paper introduces a novel SITR (Susceptible-Infected-Treated-Recovered) epidemic model that incorporates a Holling Type III incidence rate and a saturated treatment function to capture superspreading dynamics and finite healthcare capacity. We establish the model’s well-posedness by proving the positivity and boundedness of solutions. A comprehensive bifurcation analysis reveals that the system exhibits rich dynamical behaviors, including Transcritical, Saddle–node, and Hopf bifurcations, which delineate thresholds between disease extinction, persistence, and oscillatory states. An optimal control framework is subsequently formulated to derive effective intervention strategies. The core methodological contribution is the development of a hybrid deep neural network (DNN) architecture, utilizing Tanh and ReLU activations, to serve as a high-fidelity surrogate for the model’s complex dynamics. This approach is validated within a stochastic numerical scheme, employing a 70%–15%–15% data split for robust training and testing. The DNN achieves exceptional predictive accuracy, with a mean squared error of and a minimum absolute error of , demonstrating precise alignment with benchmark solutions. This work establishes a novel paradigm that integrates sophisticated dynamical systems theory with advanced deep learning, resulting in a computationally efficient and highly accurate framework for analyzing and controlling complex epidemic systems.
{"title":"Optimal control of chaos in a novel SITR epidemic model with generalized incidence and adaptive treatment dynamics: A deep neural network analysis","authors":"A. El-Mesady , M.A. Abdelkawy , Muhammad Farhan , Mohammad Izadi","doi":"10.1016/j.matcom.2025.12.005","DOIUrl":"10.1016/j.matcom.2025.12.005","url":null,"abstract":"<div><div>This paper introduces a novel SITR (Susceptible-Infected-Treated-Recovered) epidemic model that incorporates a Holling Type III incidence rate and a saturated treatment function to capture superspreading dynamics and finite healthcare capacity. We establish the model’s well-posedness by proving the positivity and boundedness of solutions. A comprehensive bifurcation analysis reveals that the system exhibits rich dynamical behaviors, including Transcritical, Saddle–node, and Hopf bifurcations, which delineate thresholds between disease extinction, persistence, and oscillatory states. An optimal control framework is subsequently formulated to derive effective intervention strategies. The core methodological contribution is the development of a hybrid deep neural network (DNN) architecture, utilizing Tanh and ReLU activations, to serve as a high-fidelity surrogate for the model’s complex dynamics. This approach is validated within a stochastic numerical scheme, employing a 70%–15%–15% data split for robust training and testing. The DNN achieves exceptional predictive accuracy, with a mean squared error of <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>10</mn></mrow></msup></mrow></math></span> and a minimum absolute error of <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>8</mn></mrow></msup></mrow></math></span>, demonstrating precise alignment with benchmark solutions. This work establishes a novel paradigm that integrates sophisticated dynamical systems theory with advanced deep learning, resulting in a computationally efficient and highly accurate framework for analyzing and controlling complex epidemic systems.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"243 ","pages":"Pages 427-467"},"PeriodicalIF":4.4,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737431","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 : 2026-05-01Epub Date: 2025-12-03DOI: 10.1016/j.matcom.2025.11.035
Jan Grošelj
The paper provides a generalization of quadratic splines over a Powell–Sabin refined triangulation to splines of any degree greater than two. The splines are constructed by imposing maximal super-smoothness at Powell–Sabin triangle split points and reproduce polynomials to the highest possible degree. The spline spaces are characterized by functionals that induce a B-spline representation over a triangulation, i.e., a representation of splines in terms of locally supported nonnegative basis functions that form a partition of unity. This makes the considered splines readily applicable in computer aided geometric design, function approximation problems, and finite element methods for solving partial differential equations.
{"title":"Higher-degree super-smooth C1 splines over a Powell–Sabin refined triangulation","authors":"Jan Grošelj","doi":"10.1016/j.matcom.2025.11.035","DOIUrl":"10.1016/j.matcom.2025.11.035","url":null,"abstract":"<div><div>The paper provides a generalization of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> quadratic splines over a Powell–Sabin refined triangulation to <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> splines of any degree greater than two. The splines are constructed by imposing maximal super-smoothness at Powell–Sabin triangle split points and reproduce polynomials to the highest possible degree. The spline spaces are characterized by functionals that induce a B-spline representation over a triangulation, i.e., a representation of splines in terms of locally supported nonnegative basis functions that form a partition of unity. This makes the considered splines readily applicable in computer aided geometric design, function approximation problems, and finite element methods for solving partial differential equations.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"243 ","pages":"Pages 382-406"},"PeriodicalIF":4.4,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737429","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 : 2026-04-01Epub Date: 2025-11-14DOI: 10.1016/j.matcom.2025.11.015
Yangrong Li, Zhiqiang Wang, Xiaowen Tang
Discrete-time Klein–Gordon–Schrödinger lattice equations are established according to implicit Euler schemes, while a family of numerical attractors is obtained when time-sizes belong to an existing interval. The continuity-set of numerical attractors under the Hausdorff distance is shown to be a dense IOD-type (Intersection of countably many Open Dense sets) in the existing interval, moreover, this continuity-set has the continuum cardinality. A common bound of all numerical attractors is provided and leads to the continuous convergence of numerical attractors as two external forces tend to zero. Finally, the global attractor of the original continuous-time system is approximated by numerical attractors in the sense of upper semicontinuity. Forward invariant sets, recursive tails estimates and Taylor’s remainders play key roles in the proofs.
{"title":"IOD-type continuity-sets and bounds of numerical attractors for discrete Klein–Gordon–Schrödinger equations","authors":"Yangrong Li, Zhiqiang Wang, Xiaowen Tang","doi":"10.1016/j.matcom.2025.11.015","DOIUrl":"10.1016/j.matcom.2025.11.015","url":null,"abstract":"<div><div>Discrete-time Klein–Gordon–Schrödinger lattice equations are established according to implicit Euler schemes, while a family of numerical attractors is obtained when time-sizes belong to an existing interval. The continuity-set of numerical attractors under the Hausdorff distance is shown to be a dense IOD-type (Intersection of countably many Open Dense sets) in the existing interval, moreover, this continuity-set has the continuum cardinality. A common bound of all numerical attractors is provided and leads to the continuous convergence of numerical attractors as two external forces tend to zero. Finally, the global attractor of the original continuous-time system is approximated by numerical attractors in the sense of upper semicontinuity. Forward invariant sets, recursive tails estimates and Taylor’s remainders play key roles in the proofs.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 19-35"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145532420","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号