Results in Applied Mathematics最新文献

英文中文

Isogeometric boundary element method for solving 2D multi-media heat conduction problems 求解二维介质热传导问题的等几何边界元法

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-11-01 Epub Date: 2025-09-23 DOI: 10.1016/j.rinam.2025.100639

Kunpeng Li , Wei Jiang , Haozhi Li

In this work, we employ the isogeometric boundary element approach to investigate heat transfer mechanisms in various media. We derive and construct integral equations for the interface of different media to address heat transfer issues. Our proposed modeling technique for two-dimensional problems can be dynamically constructed by incorporating control points and weight factors. In comparison to other numerical software, this approach offers high customizability, improves model accuracy, mitigates mesh errors, and seamlessly integrates the advantages of Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE) through the isogeometric method. The boundary element approach boasts several advantages, with numerical stability and excellent precision being paramount. The amalgamation of the isogeometric approach with the boundary element method holds promise for future applications in practical engineering. Simultaneously, we address the domain integral using the radial integration approach. The algorithmic results reveal that the isogeometric boundary element method, in contrast to the traditional boundary element method, expands the applicability of the latter while maintaining good stability and robustness. This provides substantial support for further software integration.

在这项工作中，我们采用等几何边界元方法来研究各种介质中的传热机制。我们推导并构造了不同介质界面的积分方程来解决传热问题。我们提出的二维问题建模技术可以通过结合控制点和权重因子来动态构建。与其他数值软件相比，该方法具有较高的可定制性，提高了模型精度，减轻了网格误差，并通过等几何方法无缝集成了计算机辅助设计（CAD）和计算机辅助工程（CAE）的优势。边界元法具有数值稳定性和较高的精度等优点。等几何方法与边界元方法的融合在实际工程中具有广阔的应用前景。同时，我们使用径向积分方法来处理域积分。算法结果表明，与传统边界元方法相比，等几何边界元方法在保持较好的稳定性和鲁棒性的同时，扩大了传统边界元方法的适用性。这为进一步的软件集成提供了实质性的支持。

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引用次数: 0

Efficient computation for the eigenvalues and eigenfunctions of two-dimensional non-separable linear canonical transform 二维不可分线性正则变换的特征值和特征函数的高效计算

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-11-01 Epub Date: 2025-09-27 DOI: 10.1016/j.rinam.2025.100645

Yuru Tian, Feng Zhang

The parameter matrix of the two-dimensional non-separable linear canonical transform (2D-NSLCT) determines its specific form and properties. Certain forms of the 2D-NSLCT are consistent with well-known transforms, such as two-dimensional non-separable fractional Fourier transform (2D-NSFrFT), Fresnel transform, and other related transforms. Based on the analysis of the eigenvalues and eigenfunctions of these special transforms, this paper proposes an efficient method for computing the eigenvalues and eigenfunctions of the 2D-NSLCT. Specifically, based on the properties of similar matrices, if the parameter matrix of the 2D-NSLCT is similar to that of a special transform (e.g., 2D-NSFrFT or other transforms), then the eigenvalues of the 2D-NSLCT are identical to those of the special transform. Moreover, the eigenfunctions of the 2D-NSLCT can be computed using the known eigenfunctions of this special transform based on the additivity of the 2D-NSLCT. The detailed derivation is presented in this paper, and some applications of the 2D-NSLCT’s eigenfunction are also discussed.

二维不可分线性正则变换（2D-NSLCT）的参数矩阵决定了它的具体形式和性质。2D-NSLCT的某些形式与众所周知的变换一致，例如二维不可分分数傅里叶变换（2D-NSFrFT）、菲涅耳变换和其他相关变换。在分析这些特殊变换的特征值和特征函数的基础上，提出了一种计算2D-NSLCT特征值和特征函数的有效方法。具体来说，根据相似矩阵的性质，如果2D-NSLCT的参数矩阵与特殊变换（如2D-NSFrFT或其他变换）的参数矩阵相似，则2D-NSLCT的特征值与特殊变换的特征值相同。基于2D-NSLCT的可加性，利用该特殊变换的已知特征函数可以计算2D-NSLCT的特征函数。本文给出了二维nslct特征函数的详细推导过程，并讨论了二维nslct特征函数的一些应用。

引用次数: 0

Remarks on numerical approximation of Volterra integral equations by Walsh–Hadamard transform 沃尔什-阿达玛变换对Volterra积分方程数值逼近的评述

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-11-01 Epub Date: 2025-10-03 DOI: 10.1016/j.rinam.2025.100648

Farrukh Mukhamedov , Ushangi Goginava , Akaki Goginava , James Wheeldon

Walsh functions form a piecewise-constant orthonormal basis that is particularly well-suited for digital computation and signal approximation. Nevertheless, the direct evaluation of Walsh transforms for discrete functions becomes computationally prohibitive as the resolution increases. To overcome this difficulty, we develop an efficient numerical scheme based on the Fast Walsh–Hadamard–Fourier Transform (FWHFT) for the approximation of solutions to Volterra integral equations. The proposed method reduces the computational complexity from

O (2^{2 n})

O (n 2^{n}),

thereby rendering the approach scalable to high-resolution problems. We present a complete algorithmic framework that exploits this fast transform and analyze its performance on a variety of examples. In particular, we illustrate several examples for the broad applicability of the method. These examples highlight the principal advantages of the FWHFT approach, as well as certain limitations inherent in the transform structure. As a further application, we implement the method in a financial setting by addressing the problem of pricing European options under the Bachelier model. This example demonstrates not only the accuracy of the proposed algorithm but also its practical relevance to computational finance, especially in scenarios involving structured payoff functions. Numerical experiments confirm the expected convergence behavior and the substantial computational savings afforded by the method. Finally, we discuss possible extensions of the approach to fractional-order models, which are naturally linked to Volterra-type integral equations and arise frequently in applications.

沃尔什函数形成一个分段常数标准正交基，特别适合于数字计算和信号近似。然而，随着分辨率的增加，离散函数的Walsh变换的直接评估在计算上变得令人望而却步。为了克服这一困难，我们开发了一种基于快速Walsh-Hadamard-Fourier变换（FWHFT）的有效数值格式来逼近Volterra积分方程的解。该方法将计算复杂度从0 （22n）降低到O(n2n)，从而使该方法可扩展到高分辨率问题。我们提出了一个完整的算法框架，利用这种快速变换，并分析了它在各种例子上的性能。特别地，我们举例说明了该方法的广泛适用性。这些例子突出了FWHFT方法的主要优点，以及转换结构中固有的某些限制。作为进一步的应用，我们通过解决巴舍利耶模型下的欧洲期权定价问题，在金融环境中实现了该方法。这个例子不仅证明了所提出算法的准确性，而且还证明了它与计算金融的实际相关性，特别是在涉及结构化支付函数的场景中。数值实验证实了该方法具有预期的收敛性和可观的计算节省。最后，我们讨论了分数阶模型的可能扩展，分数阶模型自然地与volterra型积分方程联系在一起，并且在应用中经常出现。

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引用次数: 0

Bayesian estimation of discretely observed diffusion processes using Wiener chaos expansion 利用维纳混沌展开的离散观测扩散过程的贝叶斯估计

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-11-01 Epub Date: 2025-09-27 DOI: 10.1016/j.rinam.2025.100644

Fernando Baltazar-Larios , Gabriel Adrián Salcedo-Varela , Francisco Delgado-Vences

We employ a Bayesian inference technique for discretely observed diffusion processes that arise as solutions of stochastic differential equations. Our aim is to estimate the parameters of the stochastic differential equation. To achieve this, we frame the estimation procedure as a missing data problem. In this framework, the complete dataset includes the theoretically continuous-time path between observed points. We propose augmenting the dataset and using a Gibbs sampler to derive Bayesian estimators for the parameters in cases where the diffusion process is observed discretely. The Gibbs sampler is integrated with a diffusion bridge simulation technique based on the Wiener chaos expansion. The methodology and its implementation are demonstrated through examples and simulation studies. We also present an application to actual data.

我们采用贝叶斯推理技术离散观察扩散过程出现作为随机微分方程的解决方案。我们的目的是估计随机微分方程的参数。为了实现这一点，我们将估计过程定义为缺失数据问题。在这个框架中，完整的数据集包含了观测点之间理论上的连续时间路径。我们建议扩大数据集并使用吉布斯采样器在离散观察扩散过程的情况下推导参数的贝叶斯估计。Gibbs采样器集成了基于维纳混沌展开的扩散桥模拟技术。通过实例和仿真研究证明了该方法及其实现。我们也给出了一个实际数据的应用。

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 Epub Date: 2025-11-25 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

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 Epub Date: 2025-11-06 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

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 Epub Date: 2025-10-28 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

Mathematical analysis of shallow water wave and the generalized Hirota-Satsuma-Ito models: Soliton solutions and their interactions 浅水波的数学分析与广义Hirota-Satsuma-Ito模型：孤子解及其相互作用

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-11-01 Epub Date: 2025-09-19 DOI: 10.1016/j.rinam.2025.100641

M. Belal Hossen , Md. Towhiduzzaman , Harun-Or-Roshid , K. M. Abdul A. Woadud

This study investigates the mathematical properties and soliton dynamics of the (2+1)-dimensional extended Shallow Water Wave (eSWW) and the generalized Hirota-Satsuma-Ito (gHSI) models by Hirota bilinear scheme. A comprehensive mathematical analysis is conducted to derive multi-soliton solutions, including 2-soliton and 3-soliton solutions, while breather, rogue and lump solutions derive from 2-soliton. Investigation focuses on soliton interactions under various conditions, with particular attention to special cases like rogue and lump type solutions, highlighting their distinct characteristics and physical significance. Additionally, the analysis extends to the gHSI equation, where long wave limit scheme is applied to attain rogue and lump wave solutions. We analyzed the planar dynamics of the system to assess its sensitivity. These findings enhance our knowledge of nonlinear wave processes, with potential applications in oceanography, fluid mechanics, and related scientific fields.

利用Hirota双线性格式研究了（2+1）维扩展浅水波（eSWW）和广义Hirota- satsuma - ito （gHSI）模型的数学性质和孤子动力学。对多孤子解进行了全面的数学分析，包括2孤子解和3孤子解，而呼吸、流氓和块状解则由2孤子导出。研究重点是各种条件下的孤子相互作用，特别关注流氓型和块状解等特殊情况，突出其独特的特征和物理意义。此外，分析扩展到gHSI方程，其中长波极限格式应用于获得流氓和块波解。我们分析了系统的平面动力学，以评估其灵敏度。这些发现增强了我们对非线性波浪过程的认识，在海洋学、流体力学和相关科学领域具有潜在的应用前景。

引用次数: 0

A Polak–Ribière–Polyak like method with restart technique for monotone nonlinear equations 单调非线性方程的polak - ribi<s:1> - polyak类方法及重启技术

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-11-01 Epub Date: 2025-10-06 DOI: 10.1016/j.rinam.2025.100646

Abdulkarim Hassan Ibrahim , Kanikar Muangchoo

This article proposes a projection-based method that combines the hyperplane technique, a restart strategy, and a modified Polak–Ribière–Polyak conjugate gradient method to solve large-scale systems of nonlinear equations. The method ensures that the search direction satisfies the sufficient descent condition at each iteration and retains a key property of the classical PRP approach. Global convergence is established under the assumptions of monotonicity and Lipschitz continuity. Numerical experiments are conducted to demonstrate the effectiveness and robustness of the proposed approach, with comparisons made against recent methods from the literature.

本文提出了一种结合超平面技术、重新启动策略和改进的polak - ribi - polyak共轭梯度法的基于投影的方法来求解大型非线性方程组。该方法保证了每次迭代的搜索方向满足充分下降条件，并保留了经典PRP方法的一个关键性质。在单调性和Lipschitz连续性假设下，建立了全局收敛性。数值实验证明了所提出的方法的有效性和鲁棒性，并与文献中最近的方法进行了比较。

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 Epub Date: 2025-10-31 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。

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