Mathematics and Computers in Simulation最新文献

{"title":"High-order hybrid computational method with adaptive mesh strategies for time-fractional nonlinear reaction–diffusion problems featuring weak singularity","authors":"Anshima Singh","doi":"10.1016/j.matcom.2025.12.017","DOIUrl":"10.1016/j.matcom.2025.12.017","url":null,"abstract":"<div><div>This research focuses on developing a hybrid computational approach that leverages high-order finite difference techniques and non-polynomial spline methods to address time-fractional nonlinear reaction–diffusion equations with bounded and unbounded temporal derivatives at time <span><math><mrow><mi>t</mi><mo>=</mo><mn>0</mn></mrow></math></span>. In particular, we study the application of the Fitzhugh–Nagumo model in analyzing the behavior of electrical impulses, as well as the generalized Fisher’s reaction–diffusion equation in modeling abnormal diffusion in biological tissues. The temporal fractional operator is approximated through a high-order scheme constructed using various interpolation approaches including linear, quadratic, and cubic interpolation, achieving <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mi>τ</mi></mrow><mrow><mo>−</mo><mrow><mo>(</mo><mn>4</mn><mo>−</mo><mi>α</mi><mo>)</mo></mrow></mrow></msubsup><mo>)</mo></mrow></mrow></math></span> precision on appropriately selected nonuniform meshes and <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mi>τ</mi></mrow><mrow><mo>−</mo><mi>α</mi></mrow></msubsup><mo>)</mo></mrow></mrow></math></span> precision on uniformly spaced meshes, where <span><math><mi>α</mi></math></span> is the order of the time-fractional derivative and <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>τ</mi></mrow></msub></math></span> denotes the number of temporal discretization points. Further, we utilize a high precision stable parametric quintic spline (PQS) for spatial discretization. The obtained nonlinear equation system is resolved through an iterative computational algorithm. The stability analysis of the fully discrete scheme is conducted on uniform distributed meshes through Fourier analysis techniques. We also prove the convergence of the proposed method for the solution with bounded and unbounded temporal derivative in the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-norm using the Fourier analysis method on uniformly distributed mesh. The convergence order is found to be <span><math><mrow><mo>(</mo><mn>4</mn><mo>−</mo><mi>α</mi><mo>)</mo></mrow></math></span> in the time direction and 4.5 in the space direction for bounded temporal derivative. Moreover, for the solutions with unbounded temporal derivatives, the accuracy achieves <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mi>τ</mi></mrow><mrow><mo>−</mo><mi>α</mi></mrow></msubsup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>4</mn><mo>.</mo><mn>5</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> theoretically on uniform mesh, which numerically delivers superior temporal accuracy of <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mi>τ</mi></mrow><mrow><mo>−</mo><mrow><mo>(</mo><mn>4</mn><mo>−</mo><mi>α</mi><mo>)</mo></mrow></mrow></msubsup>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"244 ","pages":"Pages 90-113"},"PeriodicalIF":4.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841720","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}

{"title":"IMACS Calendar of Events","authors":"","doi":"10.1016/S0378-4754(26)00037-6","DOIUrl":"10.1016/S0378-4754(26)00037-6","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"244 ","pages":"Page 265"},"PeriodicalIF":4.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146074082","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}

{"title":"Spatiotemporal dynamics and bifurcation analysis on network and non-network environments of a dangerous prey and predator model","authors":"Masoom Bhargava,&nbsp;Balram Dubey","doi":"10.1016/j.matcom.2025.12.012","DOIUrl":"10.1016/j.matcom.2025.12.012","url":null,"abstract":"<div><div>Predators in ecological systems frequently confront perilous prey, exposing themselves to the possibility of harm and jeopardizing their own life. Meanwhile, prey endeavour to maximize their reproductive success while minimizing the potential dangers. This work presents a 2D prey–predator model, considering predator interference, the negative impact of fear on prey reproduction, and the consequences of interactions with poisonous prey. The model demonstrates multistability and experiences a range of bifurcations, such as Hopf, transcritical, saddle node, Bogdanov–Takens, cusp, Bautin, and homoclinic bifurcations. The critical parameters might result in the extinction of predators if they suffer excessive losses from interactions with risky prey. It emphasizes the delicate balance that predators must maintain in order to survive. This study explores the expansion of spatial patterns in both network and non-network systems, comparing Turing pattern formation in network models with continuous media and various network topologies. It highlights how Turing patterns are influenced by predator loss, diffusion coefficients, and network topologies. Distinctive patterns, such as spots and stripes, form stably. The simulation shows how different network architectures specifically LA (Lattice), Barabási–Albert (BA), and Watts–Strogatz (WS) networks affect pattern stabilization time and node density distribution. These findings offer vital insights into understanding the complex nature of relationship among prey and predators in ecological systems.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"244 ","pages":"Pages 135-161"},"PeriodicalIF":4.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885670","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}

{"title":"A novel semi-implicit finite difference approach for the Sobolev equation with generalized Burgers-type nonlinear term","authors":"Kexin Li ,&nbsp;Hao Zhang ,&nbsp;Omid Nikan ,&nbsp;Wenlin Qiu","doi":"10.1016/j.matcom.2025.12.024","DOIUrl":"10.1016/j.matcom.2025.12.024","url":null,"abstract":"<div><div>This paper investigates the approximate solution of the Sobolev equation with generalized Burgers-type nonlinear term. For this purpose, a backward Euler (BE) semi-implicit difference approach is proposed, whose primary advantage is that, unlike general implicit finite difference (FD) schemes, it circumvents the necessity of iterative methods in computation and greatly reduces computing costs. A rigorous numerical analysis of the proposed strategy is then conducted based on the energy method. Specifically, the existence, uniqueness, and boundedness of the approximate solution are established via the Leray–Schauder theorem and discrete Sobolev’s inequality. Furthermore, the convergence and perturbation stability of the proposed strategy are derived using the discrete Gronwall inequality. Finally, the theoretical findings are corroborated through several numerical examples.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"244 ","pages":"Pages 181-195"},"PeriodicalIF":4.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885749","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}

{"title":"A highly efficient decoupled algorithm for two-phase ferrohydrodynamics model based on Gauge-Uzawa method","authors":"Kaiwen Shi ,&nbsp;Haohao Li ,&nbsp;Haiyan Su ,&nbsp;Xiaodi Zhang","doi":"10.1016/j.matcom.2025.12.007","DOIUrl":"10.1016/j.matcom.2025.12.007","url":null,"abstract":"<div><div>In this paper, we design a decoupled, linear and unconditionally energy stable algorithm for the two-phase ferrohydrodynamics (CHFHD) model. The proposed algorithm employs a semi-implicit stabilization approach to solve the phase-field equations, while the ferrohydrodynamics (FHD) part is discretized using the Gauge-Uzawa method. Furthermore, the nonlinear terms of the model are handled by stabilization method with some implicit-explicit treatments. Compared to the standard projection method, our approach resolves the issues related to the initial value selection for pressure <span><math><mi>p</mi></math></span> and the handling of artificial boundary conditions on <span><math><mi>p</mi></math></span>, which often lead to the formation of boundary layers and reduced numerical accuracy. Finally, several numerical examples are provided to demonstrate the effectiveness and validity of the proposed algorithm.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"244 ","pages":"Pages 1-18"},"PeriodicalIF":4.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792214","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}

{"title":"Optimal convergence analysis of arbitrary Lagrangian–Eulerian finite element methods in energy norm for Poisson–Nernst–Planck moving boundary problems","authors":"Xiaomeng Lin ,&nbsp;Mingyan He ,&nbsp;Pengtao Sun","doi":"10.1016/j.matcom.2025.12.020","DOIUrl":"10.1016/j.matcom.2025.12.020","url":null,"abstract":"<div><div>In this paper, an arbitrary Lagrangian–Eulerian (ALE)-based finite element method (FEM) is developed and analyzed for a class of Poisson–Nernst–Planck (PNP) moving boundary problems, where the optimal convergence rate in energy norm and suboptimal convergence rate in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm are obtained for a fully discrete, linearized, ALE-based finite element scheme. One key analytical technique is the introduction of a novel <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-projection that is associated with a coupling between the electric potential and ionic concentrations over a moving/deforming domain. Numerical experiments are carried out to validate all derived theoretical results. As a starting point, the developed ALE-finite element scheme and its analytical techniques can be extended to moving interface problems of PNP system and more beyond, of PNP–Navier–Stokes coupling system occurring in ion channels and their surrounding cellular environment that will be studied in our future work.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"244 ","pages":"Pages 162-180"},"PeriodicalIF":4.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885748","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}

{"title":"Localized complex dynamics in higher-order networks: Heterogeneous topological coupling and effective degree models","authors":"Jiahui Song ,&nbsp;Zaiwu Gong","doi":"10.1016/j.matcom.2025.12.016","DOIUrl":"10.1016/j.matcom.2025.12.016","url":null,"abstract":"<div><div>Higher-order networks have become a vital tool for delineating multi-body interactions in complex systems, offering unique capabilities for modeling contagion dynamics. However, existing research largely focuses on higher-order structures between nodes, frequently neglecting the significant role of non-higher-order areas, or \"gap regions\" in spreading processes. To address this, we propose a new framework that partitions networks into distinct \"higher-order interaction regions\" and \"gap regions\", connected by \"transition zones\". This approach facilitates a principled distinction between emergent interactive structures and conventional network constructs based on intrinsic properties. We further introduce an innovative effective degree model to refine node classification based on regional contexts and local topology. Building on this, we establish a multi-layered contagion process where infection rates depend on both the scale of neighborhood infection and microscopic transmission rates via distinct pathways. To enhance tractability, a closure-based self-consistent method is developed to transform higher-order traits into feasible closed forms, allowing systematic tracking of complex dynamics. SIS rumor propagation simulations on synthetic and empirical networks, with seeds in various regions, show that the initial source profoundly impacts the process—specifically regarding prevalence, diffusion radius, and diameter. Notably, seeding in transition zones causes more explosive and widespread outbreaks. This study deepens our understanding of dynamic diversity in higher-order networks and offers quantitative tools for strategies in rumor control and epidemic warning.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"244 ","pages":"Pages 114-134"},"PeriodicalIF":4.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841718","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}

{"title":"Complex bifurcations and new types of structure uncovered in the Qi system","authors":"Enrui Zhang,&nbsp;Xianyi Li","doi":"10.1016/j.matcom.2025.12.013","DOIUrl":"10.1016/j.matcom.2025.12.013","url":null,"abstract":"<div><div>In this paper, we revisit the Qi system and reveal its previously undiscovered complex dynamical characteristics. We first rigorously characterize the precise distribution of its equilibria in its total parameter space, then completely analyze the stability of all of its equilibria. Next, what is more important, we investigate its bifurcation problems concerning both the quantity of equilibria and stability boundaries, further analyzing codimension-two bifurcations between subcritical and supercritical pitchfork bifurcations, as well as codimension-three Hopf bifurcations. Finally, through numerical encoding of system trajectory, we generate biparametric sweep that unveils several remarkable phenomena deserving deeper exploration, where, most significantly, we first in the Qi system discover intriguing and new structures: self-similar UII-shaped structure and shrimp-shaped structure.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"244 ","pages":"Pages 226-263"},"PeriodicalIF":4.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927491","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}

{"title":"A projected PRP conjugate gradient method for constrained multiobjective optimization with application to friction stir welding","authors":"Kaiping Liu ,&nbsp;Jiawei Chen","doi":"10.1016/j.matcom.2025.12.014","DOIUrl":"10.1016/j.matcom.2025.12.014","url":null,"abstract":"<div><div>Based on the projected combined search direction, a novel projected Polak–Ribière–Polyak (PRP) conjugate gradient method is presented for constrained multiobjective optimization problems. The search direction generated by the proposed method satisfies the sufficient descent condition by adopting the truncation technique, which overcomes the operational challenges caused by nonlinear projection operators. Moreover, we establish the convergence of the proposed method without any convex assumptions, and apply the proposed method to address the multiobjective optimization problem in the friction stir welding process. Finally, numerical experiments show that the proposed method is not only of higher performance but also more suitable for solving multimodal multiobjective optimization problems.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"244 ","pages":"Pages 70-89"},"PeriodicalIF":4.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841719","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}

{"title":"News of IMACS","authors":"","doi":"10.1016/S0378-4754(26)00036-4","DOIUrl":"10.1016/S0378-4754(26)00036-4","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"244 ","pages":"Page 264"},"PeriodicalIF":4.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146074080","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}