Results in Applied Mathematics最新文献

英文中文

A local meshless technique for recovering dual forms of time-varying sources in the nonlocal inverse heat equation 非局部逆热方程中时变源对偶形式的局部无网格恢复技术

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-11-01 DOI: 10.1016/j.rinam.2025.100673

Elyas Shivanian , Ahmad Jafarabadi , Mousa J. Huntul

This study focuses on retrieving a time-dependent source term in the heat equation governed by two distinct nonlocal boundary conditions. The inverse problem is structured with an interior energy over-specification constraint. The proposed computational framework combines the partition of unity approach for spatial discretization with the finite difference scheme for temporal advancement. Through energy analysis, the semi-discrete time-stepping formulation is proven to be unconditionally stable and convergent at a rate of

O (δ t)

. Despite being linear and uniquely solvable, the problem is inherently ill-posed, as slight disturbances in input data can induce significant errors in the reconstructed solution. To counteract this instability, Tikhonov regularization is implemented, yielding a stable approximation even under noisy data conditions. Moreover, a novel parameter selection strategy for the regularization is introduced, which surpasses standard methods by delivering substantially improved results. Numerical simulations corroborate the scheme’s robustness, demonstrating its accuracy with noise-free inputs and its resilience when handling contaminated measurements.

本研究的重点是在由两个不同的非局部边界条件控制的热方程中检索与时间相关的源项。该逆问题具有内部能量超规范约束。所提出的计算框架结合了空间离散化的单位分割法和时间推进的有限差分格式。通过能量分析，证明了半离散时步公式是无条件稳定的，并以0 （δt）的速率收敛。尽管该问题是线性且唯一可解的，但它本质上是病态的，因为输入数据中的轻微干扰会在重构解中引起显著误差。为了抵消这种不稳定性，Tikhonov正则化实现，即使在有噪声的数据条件下也能产生稳定的近似。此外，引入了一种新的正则化参数选择策略，该策略通过提供显着改善的结果来超越标准方法。数值模拟证实了该方案的鲁棒性，证明了其在无噪声输入下的准确性以及在处理污染测量时的弹性。

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引用次数: 0

α-scaled strong convergence of stochastic theta method for stochastic differential equations driven by time-changed Lévy noise beyond Lipschitz continuity 时变lsamvy噪声驱动的随机微分方程的α尺度强收敛性

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-11-01 DOI: 10.1016/j.rinam.2025.100665

Jingwei Chen

This paper develops an

α

-parametrized framework for analyzing the strong convergence of the stochastic theta (ST) method for stochastic differential equations driven by time-changed Lévy noise (TCSDEwLNs). The analysis accommodates time–space-dependent coefficients satisfying local Lipschitz conditions. Properties of the inverse subordinator

E

are investigated and explicit moment bounds for the exact solution are derived with jump rate incorporated. The analysis demonstrates that the ST method converges strongly with order of

min {η_{F}, η_{G}, η_{H}, α / 2}

, establishing a precise relationship between numerical accuracy and the time-change mechanism. This theoretical advancement extends existing results and facilitates applications in finance, physics and biology where time-changed Lévy models are prevalent.

本文建立了一个α-参数化框架，用于分析时变lsamvy噪声驱动的随机微分方程随机θ (ST)方法的强收敛性。该分析考虑了满足局部利普希茨条件的时空相关系数。研究了逆次元E的性质，导出了包含跳跃率的精确解的显式矩界。分析表明，ST方法在min{ηF，ηG,ηH，α/2}阶上有很强的收敛性，建立了数值精度与时变机理之间的精确关系。这一理论的进步扩展了现有的结果，并促进了在金融、物理和生物领域的应用，在这些领域，时间变化的lsamvy模型是普遍存在的。

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引用次数: 0

Turing conditions for a two-component isotropic growing system from a potential function 二组分各向同性势函数生长系统的图灵条件

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-11-01 DOI: 10.1016/j.rinam.2025.100664

Aldo Ledesma-Durán, Consuelo García-Alcántara, Iván Santamaría-Holek

We analyze pattern formation in a two-component system within an isotropically growing or shrinking domain. By studying the evolution of a Lyapunov-like function, we derive time-dependent Turing bifurcation conditions through a stability analysis of linear perturbations across all Fourier modes. This general framework enables explicit characterization of pattern formation dynamics. Numerically, we consider two cases: a steady base state (exponential growth) and a time-dependent state (linear growth). First, we validate our approach by recovering the well-known conditions for fixed domains. Then, we simulate the Brusselator reaction system in dynamic domains, obtaining excellent agreement with our model’s predictions. These simulations highlight key pattern features, including evolution, amplitude growth, and wavenumber inertia. Our findings provide a novel energetic and geometrical perspective on the Turing bifurcation.

我们分析了各向同性增长或收缩域内双组分系统的模式形成。通过研究类李雅普诺夫函数的演化，我们通过对所有傅立叶模式的线性扰动的稳定性分析，导出了随时间变化的图灵分岔条件。这个通用框架可以明确地描述模式形成的动态。在数值上，我们考虑两种情况：稳定的基态（指数增长）和随时间变化的状态（线性增长）。首先，我们通过恢复固定域的已知条件来验证我们的方法。在此基础上，对动力学域的Brusselator反应系统进行了模拟，结果与模型的预测结果非常吻合。这些模拟突出了关键的模式特征，包括演化、振幅增长和波数惯性。我们的发现为图灵分叉提供了一种新的能量和几何视角。

引用次数: 0

Analytical solutions for time-fractional Cauchy problem based on OU, CIR and Jacobi processes with time-dependent parameters 基于OU、CIR和Jacobi过程的时间分数阶Cauchy问题解析解

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-11-01 DOI: 10.1016/j.rinam.2025.100657

Muntiranee Mongkolsin , Khamron Mekchay , Phiraphat Sutthimat

An analytical approach to solve a time-fractional Cauchy problem of order

0 < α \leq 1

based on the Ornstein–Uhlenbeck (OU), Cox–Ingersoll–Ross (CIR) and Jacobi processes with time-dependent parameters by transforming it into a system of linear fractional differential equations is established. We consider the process as an inhomogeneous Pearson diffusion and derive the analytical formulas for conditional expectations via the Volterra fractional integral equation. We also provide the

β

-conditional moments of the OU, CIR and Jacobi processes where

β \in R

. Finally, we illustrate with examples of the first and second moments of the extended OU and extended CIR processes by obtaining solutions with different

α

values and comparing to

α = 1

建立了一种基于具有时变参数的Ornstein-Uhlenbeck （OU）、Cox-Ingersoll-Ross （CIR）和Jacobi过程求解0阶<；α≤1阶时间分数阶Cauchy问题的解析方法，将其转化为线性分数阶微分方程系统。我们将此过程视为非齐次皮尔逊扩散，并通过Volterra分数阶积分方程推导出条件期望的解析公式。我们还给出了β∈R的OU、CIR和Jacobi过程的β-条件矩。最后，通过得到α值不同的解并与α=1进行比较，给出了扩展OU和扩展CIR过程的一阶矩和二阶矩的例子。

引用次数: 0

Enhancing the Euler–Maruyama integrator via a balancing strategy for stochastic Volterra integral equations 利用平衡策略增强随机Volterra积分方程的Euler-Maruyama积分器

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-11-01 DOI: 10.1016/j.rinam.2025.100671

Hassan Ranjbar, Afshin Babaei

This paper develops the balanced Euler–Maruyama integrator for stochastic Volterra integral equations. First, an upper bound for the designed integrator is rigorously established in the mean square sense. Next, the scheme is proved to give a strong convergence rate of 1/2 for general diffusion matrices. Furthermore, for a special case of diffusion matrices, we theoretically detect that the established integrator super-converges with strong order 1.0. Numerical experiments are provided to confirm the theoretical findings.

本文发展了随机Volterra积分方程的平衡Euler-Maruyama积分器。首先，在均方意义上严格地建立了所设计积分器的上界。其次，证明了该方案对于一般扩散矩阵具有1/2的强收敛速率。进一步，对于扩散矩阵的一种特殊情况，我们从理论上证明了所建立的积分器具有强阶1.0的超收敛性。数值实验验证了理论结果。

引用次数: 0

Optimal L2 error estimates of the decoupled, mass and charge-conservative mixed FEM for the two-phase inductionless MHD model 两相无感应MHD模型解耦、质量和电荷守恒混合有限元法的L2误差估计

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-11-01 DOI: 10.1016/j.rinam.2025.100662

Mengdi Du, Qinzheng Xu, Zhengkang He, Tong Zhang

This paper considers the optimal

L^{2}

-norm error estimates of numerical solutions in a decoupled, mass and charge-conservative mixed finite element method (FEM) for the two-phase inductionless MHD model, which consists of the incompressible inductionless MHD (iMHD) problem and the Cahn–Hilliard equations. Firstly, the targeted problem is split into three linear subproblems by treating the nonlinear terms in the explicit and semi-implicit schemes, and the computational size is reduced. Secondly, the unconditional stability of numerical scheme is provided by choosing different test functions and using the embedding theorem and the Cauchy inequalities. Thirdly, the optimal

L^{2}

and

H^{1}

-norms error estimates of numerical solutions are obtained based on the Ritz quasi-projection and Stokes projection. Finally, several numerical results are given to verify the established theoretical findings and show the performance of the considered numerical scheme.

本文研究了由不可压缩无感应MHD （iMHD）问题和Cahn-Hilliard方程组成的两相无感应MHD模型的解耦、质量和电荷守恒混合有限元法（FEM）数值解的最优l2范数误差估计。首先，通过处理显式和半隐式格式中的非线性项，将目标问题分解为三个线性子问题，减小了计算量；其次，通过选择不同的测试函数，利用嵌入定理和柯西不等式，给出了数值格式的无条件稳定性；第三，基于Ritz拟投影和Stokes投影得到数值解的最优L2范数和h1范数误差估计。最后，给出了几个数值结果来验证所建立的理论结果和所考虑的数值格式的性能。

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引用次数: 0

Stability and finite-time synchronization of discrete FitzHugh–Nagumo systems using Lyapunov theory 基于Lyapunov理论的离散FitzHugh-Nagumo系统的稳定性和有限时间同步

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-11-01 DOI: 10.1016/j.rinam.2025.100669

Shaher Momani , Iqbal M. Batiha , Issam Bendib , Adel Ouannas , Radwan M. Batyha

This study explores finite-time synchronization (FTS) in a discrete FitzHugh–Nagumo (FHN) reaction–diffusion system. Employing Lyapunov-based techniques and numerical simulations, we establish theoretical criteria to achieve synchronization within a finite duration. The proposed methodology involves discretization of the continuous FHN model using finite difference schemes to reformulate it into a computationally feasible framework. A tailored control strategy is introduced, ensuring rapid convergence to synchronization. Numerical results validate the theoretical framework, highlighting the critical roles of diffusion coefficients, system parameters, and control gains in shaping the spatiotemporal dynamics. The findings underscore the effectiveness of the proposed approach in applications such as neuronal network synchronization, chemical kinetics, and biological pattern formation. This study provides a robust theoretical and computational foundation for advancing FTS in reaction–diffusion systems, with practical implications across diverse scientific domains.

本研究探讨离散FitzHugh-Nagumo （FHN）反应扩散系统的有限时间同步（FTS）。采用基于李亚普诺夫的技术和数值模拟，我们建立了在有限时间内实现同步的理论准则。所提出的方法包括使用有限差分格式对连续FHN模型进行离散化，将其重新表述为计算上可行的框架。引入了定制的控制策略，确保快速收敛到同步。数值结果验证了理论框架，突出了扩散系数、系统参数和控制增益在形成时空动力学中的关键作用。这些发现强调了所提出的方法在神经网络同步、化学动力学和生物模式形成等应用中的有效性。本研究为在反应扩散系统中推进FTS提供了坚实的理论和计算基础，在不同的科学领域具有实际意义。

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引用次数: 0

Carleman linearization of differential-algebraic equations systems 微分-代数方程组的Carleman线性化

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-11-01 DOI: 10.1016/j.rinam.2025.100660

Marcos A. Hernández-Ortega , C.M. Rergis , A. Román-Messina , Erlan R. Murillo-Aguirre

Carleman linearization is a mathematical technique that transforms nonlinear dynamical systems into infinite-dimensional linear systems, enabling simplified analysis. Initially developed for ordinary differential equations (ODEs) and later extended to partial differential equations (PDEs), it has found applications in control theory, biological systems, fluid dynamics, quantum mechanics, finance, and machine learning. This paper extends Carleman linearization to differential-algebraic equation (DAE) systems by introducing auxiliary functions and projecting the resulting system onto a higher-order ODE representation. Theoretical foundations are presented along with conditions under which the transformation is valid. The method is demonstrated on synthetic DAE examples, highlighting its effectiveness even when projection from algebraic variables to state variables is nontrivial or undefined.

卡尔曼线性化是一种将非线性动力系统转化为无限维线性系统的数学技术，可以简化分析。它最初用于常微分方程（ode），后来扩展到偏微分方程（PDEs），已在控制理论、生物系统、流体动力学、量子力学、金融和机器学习中得到应用。本文通过引入辅助函数，将Carleman线性化扩展到微分代数方程（DAE）系统，并将得到的系统投影到一个高阶ODE表示上。提出了理论基础，并给出了变换有效的条件。该方法在合成DAE实例上得到了验证，即使从代数变量到状态变量的投影是非平凡的或未定义的，也强调了它的有效性。

引用次数: 0

Global existence of solutions to a hyperbolic-elliptic chemotaxis model on networks with nonhomogeneous boundary conditions 非齐次边界条件下网络上双曲-椭圆趋化性模型解的整体存在性

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-11-01 DOI: 10.1016/j.rinam.2025.100668

Yafeng Li

In this paper, we investigate a coupled hyperbolic-elliptic chemotaxis system posed on a network under nonhomogeneous boundary conditions. First, the boundary data are homogenized via a linear transformation. We then establish the local existence and uniqueness of solutions by combining analytic semigroup theory with the Lax–Milgram theorem. Finally, using sharp

L^{p}

-estimates and Gronwall’s inequality, we show that sufficiently small initial data and boundary values lead to the existence of a unique nonnegative global solution.

本文研究了非齐次边界条件下网络上的双曲-椭圆耦合趋化系统。首先通过线性变换对边界数据进行均匀化处理。然后将解析半群理论与Lax-Milgram定理相结合，建立了解的局部存在唯一性。最后，利用锐利的lp估计和Gronwall不等式，我们证明了足够小的初始数据和边界值导致存在唯一的非负全局解。

引用次数: 0

Inertial forward-reflected-backward method for solving bilevel variational inequality problem 求解两级变分不等式问题的惯性前向反射-后向法

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-11-01 DOI: 10.1016/j.rinam.2025.100658

K.O. Okorie , C. Izuchukwu , C.C. Okeke , K.C. Ukandu , M. Aphane

We introduce an inertial forward-reflected-backward method for solving the bilevel variational inequality problem. Our method involves a single projection onto the feasible set and one functional evaluation, which makes it cost-effective and efficient. The inertial technique in our algorithm improves its speed of convergence, and hence our algorithm performs faster than methods without inertial effect. Under moderate conditions, we obtain strong convergence of our algorithm. Lastly, we highlight the superior performance of our algorithm in comparison with other algorithms in the literature through our numerical experiments.

介绍了一种求解二电平变分不等式问题的惯性前向反射-后向方法。该方法只需要在可行集上进行一次投影和一次函数评估，具有较高的成本效益和效率。在算法中引入惯性效应，提高了算法的收敛速度，因此算法的收敛速度比没有惯性效应的算法要快。在中等条件下，我们得到了算法的强收敛性。最后，我们通过数值实验强调了我们的算法与文献中其他算法相比的优越性能。

引用次数: 0

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