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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
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
{"title":"Isogeometric boundary element method for solving 2D multi-media heat conduction problems","authors":"Kunpeng Li ,&nbsp;Wei Jiang ,&nbsp;Haozhi Li","doi":"10.1016/j.rinam.2025.100639","DOIUrl":"10.1016/j.rinam.2025.100639","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100639"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145119769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
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
{"title":"Efficient computation for the eigenvalues and eigenfunctions of two-dimensional non-separable linear canonical transform","authors":"Yuru Tian,&nbsp;Feng Zhang","doi":"10.1016/j.rinam.2025.100645","DOIUrl":"10.1016/j.rinam.2025.100645","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100645"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
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
{"title":"Remarks on numerical approximation of Volterra integral equations by Walsh–Hadamard transform","authors":"Farrukh Mukhamedov ,&nbsp;Ushangi Goginava ,&nbsp;Akaki Goginava ,&nbsp;James Wheeldon","doi":"10.1016/j.rinam.2025.100648","DOIUrl":"10.1016/j.rinam.2025.100648","url":null,"abstract":"<div><div>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 <em>Fast Walsh–Hadamard–Fourier Transform</em> (FWHFT) for the approximation of solutions to Volterra integral equations. The proposed method reduces the computational complexity from <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> to <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>n</mi><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow><mo>,</mo></mrow></math></span> 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.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100648"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
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
{"title":"Bayesian estimation of discretely observed diffusion processes using Wiener chaos expansion","authors":"Fernando Baltazar-Larios ,&nbsp;Gabriel Adrián Salcedo-Varela ,&nbsp;Francisco Delgado-Vences","doi":"10.1016/j.rinam.2025.100644","DOIUrl":"10.1016/j.rinam.2025.100644","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100644"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
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
{"title":"Enhancing the Euler–Maruyama integrator via a balancing strategy for stochastic Volterra integral equations","authors":"Hassan Ranjbar,&nbsp;Afshin Babaei","doi":"10.1016/j.rinam.2025.100671","DOIUrl":"10.1016/j.rinam.2025.100671","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100671"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145614875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
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
{"title":"Analytical solutions for time-fractional Cauchy problem based on OU, CIR and Jacobi processes with time-dependent parameters","authors":"Muntiranee Mongkolsin ,&nbsp;Khamron Mekchay ,&nbsp;Phiraphat Sutthimat","doi":"10.1016/j.rinam.2025.100657","DOIUrl":"10.1016/j.rinam.2025.100657","url":null,"abstract":"<div><div>An analytical approach to solve a time-fractional Cauchy problem of order <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>α</mi><mo>≤</mo><mn>1</mn></mrow></math></span> 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 <span><math><mi>β</mi></math></span>-conditional moments of the OU, CIR and Jacobi processes where <span><math><mrow><mi>β</mi><mo>∈</mo><mi>R</mi></mrow></math></span>. Finally, we illustrate with examples of the first and second moments of the extended OU and extended CIR processes by obtaining solutions with different <span><math><mi>α</mi></math></span> values and comparing to <span><math><mrow><mi>α</mi><mo>=</mo><mn>1</mn></mrow></math></span>.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100657"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145466217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
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
{"title":"Optimal L2 error estimates of the decoupled, mass and charge-conservative mixed FEM for the two-phase inductionless MHD model","authors":"Mengdi Du,&nbsp;Qinzheng Xu,&nbsp;Zhengkang He,&nbsp;Tong Zhang","doi":"10.1016/j.rinam.2025.100662","DOIUrl":"10.1016/j.rinam.2025.100662","url":null,"abstract":"<div><div>This paper considers the optimal <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-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 <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-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.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100662"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145417118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
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
{"title":"Mathematical analysis of shallow water wave and the generalized Hirota-Satsuma-Ito models: Soliton solutions and their interactions","authors":"M. Belal Hossen ,&nbsp;Md. Towhiduzzaman ,&nbsp;Harun-Or-Roshid ,&nbsp;K. M. Abdul A. Woadud","doi":"10.1016/j.rinam.2025.100641","DOIUrl":"10.1016/j.rinam.2025.100641","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100641"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145098083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
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
{"title":"A Polak–Ribière–Polyak like method with restart technique for monotone nonlinear equations","authors":"Abdulkarim Hassan Ibrahim ,&nbsp;Kanikar Muangchoo","doi":"10.1016/j.rinam.2025.100646","DOIUrl":"10.1016/j.rinam.2025.100646","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100646"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
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
{"title":"Carleman linearization of differential-algebraic equations systems","authors":"Marcos A. Hernández-Ortega ,&nbsp;C.M. Rergis ,&nbsp;A. Román-Messina ,&nbsp;Erlan R. Murillo-Aguirre","doi":"10.1016/j.rinam.2025.100660","DOIUrl":"10.1016/j.rinam.2025.100660","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100660"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145417119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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