Mathematics and Computers in Simulation最新文献

英文中文

Shifted Chebyshev collocation with CESTAC-CADNA-based instability detection for nonlinear Volterra–Hammerstein integral equations 基于cestac - cadna的非线性Volterra-Hammerstein积分方程不稳定性检测的移位Chebyshev搭配

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-28 DOI: 10.1016/j.matcom.2026.01.029

Walid Remili , Samad Noeiaghdam

This paper introduces a high-order numerical method for the solution of nonlinear Volterra–Hammerstein integral equations (NVHIEs) with smooth and weakly singular kernels, based on the collocation approach. The proposed method employs a collocation scheme with shifted Chebyshev polynomials (SCPs), combined with an appropriate variable transformation, to reduce the integral equation to a nonlinear algebraic system. We rigorously analyze the convergence properties of the collocation method, establishing its theoretical validity and proving a specific convergence rate of

O (N^{3 / 4 - m})

, which highlights the rigor and efficiency of the approach. To ensure reliable error control and stability, we integrate the CESTAC (Contrôle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library, providing a unified framework that identifies numerical instabilities (self-validation, mathematical, branching, and intrinsic) while also determining the optimal step size, optimal approximation, and optimal error. Several numerical examples are presented and compared with existing methods to illustrate the enhanced efficiency and accuracy of our approach.

本文介绍了一种基于配点法求解光滑弱奇异核非线性Volterra-Hammerstein积分方程的高阶数值方法。该方法采用平移切比雪夫多项式（SCPs）搭配方案，结合适当的变量变换，将积分方程简化为非线性代数系统。我们严格分析了该方法的收敛性，建立了该方法的理论有效性，并证明了其特定的收敛速度为0 (N3/4−m)，从而突出了该方法的严谨性和有效性。为了确保可靠的误差控制和稳定性，我们集成了CESTAC （Contrôle et Estimation Stochastique des Arrondis de Calculs）方法和CADNA（精度控制和数值应用调试）库，提供了一个统一的框架，可以识别数值不稳定性（自我验证、数学、分支和内在），同时确定最佳步长、最佳近似和最佳误差。给出了几个数值算例，并与现有方法进行了比较，以说明本文方法提高了效率和精度。

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引用次数: 0

IMACS Calendar of Events IMACS事件日历

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-28 DOI: 10.1016/S0378-4754(26)00037-6

引用次数: 0

News of IMACS IMACS新闻

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-28 DOI: 10.1016/S0378-4754(26)00036-4

引用次数: 0

Approximation of generalized time fractional derivatives: Error analysis via scale and weight functions 广义时间分数阶导数的近似：通过尺度和权重函数的误差分析

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-24 DOI: 10.1016/j.matcom.2026.01.027

Vikash Sharma, Vineet Kumar Singh

In this manuscript, we investigate various properties of the Generalized time fractional derivative (GTFD). We establish several regularity results and derive bounds in specific spaces like

C^{1}, W^{1, 1}

that characterize the behavior of the GTFD operator. Furthermore, we propose an efficient hybrid computational approximation to approximate the GTFD of order

α \in (0, 1)

, applicable to smooth and non-smooth solutions. This approximation is based on a Newton interpolation polynomial of arbitrary finite degree. The role of scale and weight functions in influencing the local truncation error and convergence order is thoroughly analyzed, with numerical experiments providing validation of these theoretical insights. The proposed approximation is further utilized to construct a computational scheme for solving the general time fractional diffusion equation (GTFDE), for which we rigorously establish uniqueness and convergence, while stability is proven specifically for linear interpolation. Numerical examples are utilized to verify that our scheme is more efficient compared to the existing schemes (Stynes et al., 2017, Z. wang, 2025 and Xu et al., 2013). Without loss of generality, numerical results are presented for linear and quadratic interpolation, confirming the approximation’s accuracy and consistency with theoretical predictions.

本文研究了广义时间分数阶导数（GTFD）的各种性质。我们建立了几个正则性结果，并在C1，W1,1等特定空间中推导了表征GTFD算子行为的界。此外，我们提出了一种有效的混合计算近似来近似阶α∈(0,1)的GTFD，适用于光滑和非光滑解。这种近似是基于任意有限次的牛顿插值多项式。深入分析了尺度函数和权函数对局部截断误差和收敛阶的影响，并通过数值实验验证了这些理论见解。进一步利用所提出的近似构造了求解一般时间分数扩散方程（GTFDE）的计算格式，并严格建立了该格式的唯一性和收敛性，同时证明了该格式在线性插值下的稳定性。数值算例验证了我们的方案比现有方案更高效（Stynes et al., 2017， Z. wang, 2025 and Xu et al., 2013）。在不丧失一般性的情况下，给出了线性和二次插值的数值结果，证实了近似的准确性和与理论预测的一致性。

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引用次数: 0

Dynamics analysis of a Filippov Lymantria dispar-Great tit model with double Allee effects and two-thresholds control 具有双Allee效应和双阈值控制的Filippov Lymantria差异-大山雀模型的动力学分析

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-23 DOI: 10.1016/j.matcom.2026.01.028

Xiaoquan Kong , Ruizhi Yang

This study focuses on the Lymantria dispar-Great tit ecosystem, constructing a Filippov model with double Allee effects and proposing an integrated control strategy based on two thresholds for both pest density and natural enemy abundance. Through stability analysis of equilibria and sliding mode dynamics, the study reveals the existence of multiple sliding segments and pseudo-equilibria in the system, which can induce rich sliding bifurcation behaviors. Further investigation uncovers complex dynamical patterns under different threshold conditions, including sliding bifurcations as well as local and global bifurcations. Partial Rank Correlation Coefficient based global sensitivity analysis identifies key parameters influencing the system dynamics. The research demonstrates that appropriate setting of these two thresholds is crucial for achieving sustainable control of Lymantria dispar, while the synergistic effect of biological control and natural enemy release is essential for maintaining ecological balance.

本文以Lymantria - great tit生态系统为研究对象，构建了具有双Allee效应的Filippov模型，提出了基于害虫密度和天敌丰度两个阈值的综合防治策略。通过平衡态和滑模动力学稳定性分析，揭示了系统中存在多个滑动段和伪平衡态，从而引发丰富的滑动分岔行为。进一步的研究揭示了不同阈值条件下复杂的动力学模式，包括滑动分岔以及局部和全局分岔。基于偏秩相关系数的全局敏感性分析识别出影响系统动力学的关键参数。研究表明，合理设置这两个阈值对于实现野毒的可持续控制至关重要，而生物防治与天敌释放的协同效应对于维持生态平衡至关重要。

引用次数: 0

Multivalued extension of the Caristi-type theorem in semi-metric spaces and its numerical simulation 半度量空间中caristi型定理的多值推广及其数值模拟

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-22 DOI: 10.1016/j.matcom.2026.01.026

Pradip Debnath

We present a novel extension of the Caristi-type fixed point theorem recently established by Zubelevich (2025) for single-valued mappings on complete semi-metric spaces to the multivalued setting. Specifically, we prove that, in a complete semi-metric space

R

, if a set-valued mapping

F : R \to 2^{R}

satisfies a generalized Caristi-type inequality involving a family of lower semi-continuous, bounded-from-below functions and a semi-metric structure, then

F

admits a fixed point. Our approach constructs a suitable selection from the multivalued map and applies Zubelevich’s partial order method in conjunction with Zorn’s lemma to ensure the existence of a fixed point. Furthermore, we establish a multivalued counterpart to Zubelevich’s noncompactness theorem: if one of the associated potential functions fails to attain its minimum, then the fixed point set of

F

is necessarily noncompact. These results provide the first known multivalued Caristi-type fixed point framework for semi-metric spaces, unifying and generalizing prior work in both metric and topological vector space settings. The results are further validated by a numerical simulation showing convergence of iterates under deterministic selections.

本文将Zubelevich（2025）最近建立的关于完备半度量空间上单值映射的caristi型不动点定理推广到多值集。具体地，我们证明了在完备半度量空间R中，如果集值映射F:R→2R满足涉及下半连续、下有界函数和半度量结构的广义caristi型不等式，则F允许一个不动点。我们的方法从多值映射中构造一个合适的选择，并将Zubelevich的偏序方法与Zorn引理相结合来保证不动点的存在性。进一步，我们建立了非紧性定理的一个多值对应物：如果其中一个相关的势函数不能达到其极小值，则F的不动点集必然是非紧的。这些结果提供了已知的第一个半度量空间的多值caristi型不动点框架，统一和推广了度量和拓扑向量空间设置中的先前工作。数值模拟结果进一步验证了确定性选择下迭代的收敛性。

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引用次数: 0

Pattern formation of the Holling–Tanner model with top-hat kernel functions on square domains 方形域上顶帽核函数Holling-Tanner模型的模式形成

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-21 DOI: 10.1016/j.matcom.2026.01.025

Daifeng Duan , Biao Liu , Junjie Wei

We investigate the effects of periodic boundary conditions on a nonlocal Holling–Tanner model defined on a square domain. A top-hat kernel function with finite support is employed to characterize nonlocal interactions, which we further adapt to accommodate periodic boundary conditions. Subsequently, we derive the Turing and spatiotemporal Hopf bifurcation curves and conduct numerical simulations across the parameter ranges delineated by these curves. Our findings demonstrate substantial differences in spatiotemporal patterns between the square domain and the one-dimensional case, including squares, stripes, mixed states, irregular spot-like hexagonal patterns, and coexistence states of three-stripes and spots. These observed patterns exhibit remarkable consistency with both chemical experimental results and the skin pigmentation patterns of fish, thereby offering valuable theoretical insights and predictive frameworks for understanding spatiotemporal patterns in chemical and biological systems.

研究了周期边界条件对定义在方形域上的非局部Holling-Tanner模型的影响。采用有限支持的顶帽核函数来描述非局部相互作用，并进一步适应周期边界条件。随后，我们推导了图灵和时空Hopf分岔曲线，并在这些曲线所描绘的参数范围内进行了数值模拟。我们的研究结果表明，方形域与一维情况下的时空模式存在显著差异，包括正方形、条纹、混合状态、不规则点状六边形模式以及三条纹和斑点共存状态。这些观察到的模式与化学实验结果和鱼类皮肤色素沉着模式具有显著的一致性，从而为理解化学和生物系统的时空模式提供了有价值的理论见解和预测框架。

引用次数: 0

FEM-MsFEM for an interface-coupled parabolic problem 界面耦合抛物问题的FEM-MsFEM

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-20 DOI: 10.1016/j.matcom.2026.01.023

Jiaping Yu , Wenhan Zhang , Ren Zhao , Haibiao Zheng

In this paper, we propose and analyze a finite element coupled multiscale finite element method (FEM-MsFEM) for an interface-coupled parabolic problem. The problem involves a coefficient with multiscale characteristics in one region and in the other region without such feature. Our algorithm consists of two main steps: first, solving for the multiscale basis functions in the multiscale region via parallel computation; and second, decoupling the interface-coupled parabolic problem using a data-passing partitioned scheme. This approach allows for the problem to be solved on relatively coarse grids, thereby reducing computational costs. Under suitable assumptions for the multiscale coefficient, we establish the unconditional stability and provide error estimates for the algorithm. The effectiveness of our method is demonstrated through several numerical experiments.

本文提出并分析了一种求解界面耦合抛物问题的有限元耦合多尺度有限元方法。该问题涉及一个区域具有多尺度特征的系数，而在另一个区域不具有多尺度特征的系数。该算法主要包括两个步骤：首先，通过并行计算求解多尺度区域内的多尺度基函数；其次，采用数据传递分区方案对接口耦合抛物问题进行解耦。这种方法允许在相对粗糙的网格上解决问题，从而减少计算成本。在适当的多尺度系数假设下，建立了算法的无条件稳定性，并给出了算法的误差估计。通过数值实验验证了该方法的有效性。

引用次数: 0

Dynamic interplay of Allee effect and harvesting in a diseased amensalism model: Unraveling ecological complexity 在一个患病的仙人掌模型中，Allee效应和收获的动态相互作用：解开生态复杂性

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-19 DOI: 10.1016/j.matcom.2026.01.021

Sarita Bugalia , Sandeep Kumar , Jai Prakash Triapthi , Maia Martcheva

In this paper, we analyze the dynamics of an eco-epidemiological amensalism model involving three species, where the first species exhibits a weak Allee effect. In contrast, the second and third species are subjected to proportional harvesting. The proposed model assumes that the disease only affects the second species while the first species remains unaffected. We consider harvesting as a control parameter for both disease and amensalism dynamics. The amensalism functional response is modeled using the Holling type II response, while disease transmission follows a saturation incidence rate. Our primary mathematical objectives are to analyze the effects of the Allee parameter and harvesting on the system’s dynamics. By treating key parameters as bifurcation and threshold variables, the stability of all equilibria and the associated bifurcations are analyzed. The model exhibits a degenerate Bogdanov–Takens (BT), two saddle–node and three transcritical bifurcations. Conditions for both extinction and persistence are derived in terms of the harvesting rate. A critical threshold of harvesting is identified, beyond which the diseased species declines and the disease-free equilibrium becomes stable. Our findings reveal an upper limit of harvesting within which all species can coexist. However, the coexistence of all three species depends on initial conditions, leading to bistability. Notably, the Allee effect acts only on the first species, underlies the occurrence of a saddle–node bifurcation and eliminating equilibria for a certain parameter range, while leaving the other two species unaffected. These results provide quantitative insights into the interplay between the Allee effect and harvesting in shaping species coexistence and system dynamics.

本文分析了一个包含三种物种的生态流行病学模式的动态，其中第一种物种表现出弱的Allee效应。相比之下，第二种和第三种是按比例采伐的。提出的模型假设疾病只影响第二种物种，而第一种物种不受影响。我们认为收获是疾病和营养动力学的控制参数。amsalism功能反应使用Holling II型反应建模，而疾病传播遵循饱和发生率。我们的主要数学目标是分析Allee参数和收获对系统动力学的影响。通过将关键参数作为分岔变量和阈值变量，分析了所有平衡点的稳定性和相关的分岔。该模型具有一个简并Bogdanov-Takens （BT）、两个鞍节点和三个跨临界分叉。灭绝和持久的条件都是根据采伐率推导出来的。确定了收获的临界阈值，超过该阈值，患病物种减少，无病平衡变得稳定。我们的发现揭示了所有物种可以共存的采伐上限。然而，这三个物种的共存依赖于初始条件，导致双稳态。值得注意的是，Allee效应仅作用于第一个物种，这是鞍节点分岔和在一定参数范围内消除平衡的基础，而其他两个物种不受影响。这些结果提供了定量的见解，在形成物种共存和系统动力学的Allee效应和收获之间的相互作用。

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引用次数: 0

An insight on some properties of high order nonstandard linear multistep methods 关于高阶非标准线性多步方法若干性质的认识

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-17 DOI: 10.1016/j.matcom.2026.01.015

B. Takacs

In this paper, nonstandard multistep methods are considered. It is shown that under some (sufficient and necessary) conditions, these methods attain the same order as their standard counterpart — to prove this statement, a nonstandard version of Taylor’s series is constructed. The preservation of some qualitative properties (boundedness, the linear combination of the components, and a property similar to monotonicity) is also proven for all step sizes. The methods are applied to a one-dimensional equation and a system of equations, in which the numerical experiments confirm the theoretical results.

本文考虑了非标准多步法。证明了在某些（充分必要）条件下，这些方法与它们的标准对应物获得相同的阶数——为了证明这一说法，构造了一个非标准版本的泰勒级数。对于所有步长，还证明了一些定性性质（有界性，分量的线性组合以及类似于单调性的性质）的保留。将该方法应用于一维方程和方程组，并通过数值实验验证了理论结果。

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全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

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