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Solutions of Volterra–Fredholm type fractional integro-differential equations in terms of shifted Gegenbauer wavelets compared with the solutions by Genocchi polynomial method 移位Gegenbauer小波的Volterra-Fredholm型分数阶积分微分方程解与genochi多项式解的比较
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-09-15 DOI: 10.1016/j.cam.2025.117056
Serenay Abalı, Ali Konuralp
{"title":"Solutions of Volterra–Fredholm type fractional integro-differential equations in terms of shifted Gegenbauer wavelets compared with the solutions by Genocchi polynomial method","authors":"Serenay Abalı,&nbsp;Ali Konuralp","doi":"10.1016/j.cam.2025.117056","DOIUrl":"10.1016/j.cam.2025.117056","url":null,"abstract":"<div><div>This research introduces a novel numerical technique based on shifted Gegenbauer wavelets for solving Fredholm–Volterra fractional integro-differential equations (FVFIDEs), a class characterized by the presence of both Fredholm and Volterra integral parts. By assuming properties of the fractional derivative and applying the wavelet solution directly to the equation, the problem is transferred to finding the family of solutions of the system of algebraic equations, whose solutions are the coefficients of the series of wavelet solutions. The accuracy and efficiency of the Gegenbauer wavelet approach are primarily evaluated through a direct comparison against solutions generated using the Genocchi polynomials method for established test problems. The study demonstrates that the shifted Gegenbauer wavelet method provides precise and effective solutions, which were analyzed under varying resolution parameters and degrees of Gegenbauer polynomials.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117056"},"PeriodicalIF":2.6,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110021","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}
引用次数: 0
Improvement of Sinc-collocation methods for Volterra-Fredholm integral equations of the second kind and their theoretical analysis 第二类Volterra-Fredholm积分方程的c-配点法改进及其理论分析
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-09-15 DOI: 10.1016/j.cam.2025.117055
Tomoaki Okayama
{"title":"Improvement of Sinc-collocation methods for Volterra-Fredholm integral equations of the second kind and their theoretical analysis","authors":"Tomoaki Okayama","doi":"10.1016/j.cam.2025.117055","DOIUrl":"10.1016/j.cam.2025.117055","url":null,"abstract":"<div><div>Sinc-collocation methods for Volterra-Fredholm integral equations of the second kind were proposed independently by multiple authors: by Shamloo et al. in 2012 and by Mesgarani and Mollapourasl in 2013. Their theoretical analyses and numerical experiments suggest that the presented methods can attain root-exponential convergence. However, their convergence has not been strictly proved. This study improves these methods to facilitate implementation, and provides a convergence theorem for the improved method. For the same equations, another Sinc-collocation method was proposed in 2016 by John and Ogbonna, which is regarded as an improvement to the variable transformation employed by Shamloo et al. It may attain a higher rate than the previous methods, but its convergence has not yet been proved. Therefore, this study improves it to facilitate implementation, and provides a convergence theorem for the improved method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117055"},"PeriodicalIF":2.6,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145098654","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}
引用次数: 0
Analysis of structured deep kernel networks 结构化深度核网络分析
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-09-15 DOI: 10.1016/j.cam.2025.116975
Tizian Wenzel , Gabriele Santin , Bernard Haasdonk
{"title":"Analysis of structured deep kernel networks","authors":"Tizian Wenzel ,&nbsp;Gabriele Santin ,&nbsp;Bernard Haasdonk","doi":"10.1016/j.cam.2025.116975","DOIUrl":"10.1016/j.cam.2025.116975","url":null,"abstract":"<div><div>In this paper, we leverage a recent deep kernel representer theorem to connect kernel based learning and (deep) neural networks in order to understand their interplay. In particular, we show that the use of special types of kernels yields models reminiscent of neural networks that are founded in the same theoretical framework of classical kernel methods, while benefiting from the computational advantages of deep neural networks. Especially the introduced Structured Deep Kernel Networks (SDKNs) can be viewed as neural networks (NNs) with optimizable activation functions obeying a representer theorem. This link allows us to analyze also NNs within the framework of kernel networks. We prove analytic properties of the SDKNs which show their universal approximation properties in three different asymptotic regimes of unbounded number of centers, width and depth. Especially in the case of unbounded depth, more accurate constructions can be achieved using fewer layers compared to corresponding constructions for ReLU neural networks. This is made possible by leveraging properties of kernel approximation.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 116975"},"PeriodicalIF":2.6,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269745","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}
引用次数: 0
Energy dissipation and maximum-bound principle of the variable-step L2-1σ scheme for the time-fractional Allen–Cahn equation with general nonlinear potential 具有一般非线性势的时间分数阶Allen-Cahn方程变步长L2-1σ格式的能量耗散和最大界原理
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-09-15 DOI: 10.1016/j.cam.2025.117054
Dongdong Hu , Minghua Chen , Huiling Jiang , Haorong Huang
{"title":"Energy dissipation and maximum-bound principle of the variable-step L2-1σ scheme for the time-fractional Allen–Cahn equation with general nonlinear potential","authors":"Dongdong Hu ,&nbsp;Minghua Chen ,&nbsp;Huiling Jiang ,&nbsp;Haorong Huang","doi":"10.1016/j.cam.2025.117054","DOIUrl":"10.1016/j.cam.2025.117054","url":null,"abstract":"<div><div>In this study, we focus on a numerical scheme that maintains both the energy-dissipation law and the maximum-bound principle for the time-fractional Allen–Cahn equation with a general nonlinear potential. We propose a stabilized linear iterative method, using the variable-step L2-<span><math><msub><mrow><mn>1</mn></mrow><mrow><mi>σ</mi></mrow></msub></math></span> formula for the discretization of the Caputo fractional derivative in time and the central finite difference method for the spatial Laplacian. Furthermore, graded meshes are utilized to address the initial singularity and adaptive strategies are used to capture multiscale behavior. The proposed method is demonstrated to preserve the energy-dissipation law and maximum-bound principle in discrete settings. With the help of the maximum boundedness of the numerical solution, we derive the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>-norm error estimate of the proposed scheme by using the discrete fractional Gönwall inequality. Finally, we provide extensive numerical results to verify the theoretical results and computational efficiency of the proposed scheme.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117054"},"PeriodicalIF":2.6,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145095882","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}
引用次数: 0
An innovative neutrosophic logic adaptive high-order zeroing neural network for solving linear matrix equations: Applications to acoustic source tracking 求解线性矩阵方程的创新嗜中性逻辑自适应高阶归零神经网络：在声源跟踪中的应用
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-09-13 DOI: 10.1016/j.cam.2025.117058
Houssem Jerbi , Sondess Ben Aoun , Rabeh Abbassi , Mourad Kchaou , Theodore E. Simos , Spyridon D. Mourtas , Shuai Li , Xinwei Cao , Vasilios N. Katsikis
{"title":"An innovative neutrosophic logic adaptive high-order zeroing neural network for solving linear matrix equations: Applications to acoustic source tracking","authors":"Houssem Jerbi ,&nbsp;Sondess Ben Aoun ,&nbsp;Rabeh Abbassi ,&nbsp;Mourad Kchaou ,&nbsp;Theodore E. Simos ,&nbsp;Spyridon D. Mourtas ,&nbsp;Shuai Li ,&nbsp;Xinwei Cao ,&nbsp;Vasilios N. Katsikis","doi":"10.1016/j.cam.2025.117058","DOIUrl":"10.1016/j.cam.2025.117058","url":null,"abstract":"<div><div>Scholars have put a lot of emphasis on time-varying linear matrix equations (LMEs) problems because of its importance in science and engineering. The problem of determining the time-varying LME’s minimum-norm least-squares solution (MLLE) is therefore tackled in this work. This is achieved by the use of NHZNN, a recently developed neutrosophic logic/fuzzy adaptive high-order zeroing neural network technique. The NHZNN is an advancement on the conventional zeroing neural network (ZNN) technique, which has shown great promise in solving time-varying tasks. To address the MLLE task for arbitrary-dimensional time-varying matrices, three novel ZNN models are presented. The models perform exceptionally well, as demonstrated by two simulation studies and two real-world applications to acoustic source tracking.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117058"},"PeriodicalIF":2.6,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145095883","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}
引用次数: 0
On a wider class of second-order Bernstein-like operators 一类二阶类伯恩斯坦算子
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-09-13 DOI: 10.1016/j.cam.2025.117060
Beatrice Azzarone, Paola Lamberti
{"title":"On a wider class of second-order Bernstein-like operators","authors":"Beatrice Azzarone,&nbsp;Paola Lamberti","doi":"10.1016/j.cam.2025.117060","DOIUrl":"10.1016/j.cam.2025.117060","url":null,"abstract":"<div><div>This paper presents a wider class of the generalized Bernstein operators presented in Khosravian-Arab et al. (2018), in particular for the ones guaranteeing the second-order approximation property. Numerical results confirm the theoretical approximation order, depending on the choice of a real parameter <span><math><mi>h</mi></math></span>, characterizing such a further generalization.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117060"},"PeriodicalIF":2.6,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145098653","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}
引用次数: 0
On the expressivity of the ExSpliNet KAN model 关于ExSpliNet KAN模型的表达性
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-09-12 DOI: 10.1016/j.cam.2025.117053
Daniele Fakhoury, Hendrik Speleers
{"title":"On the expressivity of the ExSpliNet KAN model","authors":"Daniele Fakhoury,&nbsp;Hendrik Speleers","doi":"10.1016/j.cam.2025.117053","DOIUrl":"10.1016/j.cam.2025.117053","url":null,"abstract":"<div><div>ExSpliNet is a neural network model that combines ideas of Kolmogorov networks, ensembles of probabilistic trees, and multivariate B-spline representations. In this paper, we study the expressivity of the ExSpliNet model and present two constructive approximation results that mitigate the curse of dimensionality. More precisely, we prove new error bounds for the ExSpliNet approximation of a subset of multivariate continuous functions and also of multivariate generalized bandlimited functions. The main ingredients of the proofs are a constructive version of the Kolmogorov superposition theorem, Maurey’s theorem, and spline approximation results. The curse of dimensionality is lessened in the first case, while it is completely overcome in the second case. Since the considered ExSpliNet model can be regarded as a particular version of the recently introduced neural network architecture called Kolmogorov–Arnold network (KAN), our results also provide insights into the analysis of the expressivity of KANs.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117053"},"PeriodicalIF":2.6,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145098655","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}
引用次数: 0
Efficient numerical computations for solving high-dimensional stochastic differential equations 求解高维随机微分方程的有效数值计算
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-09-11 DOI: 10.1016/j.cam.2025.117043
Yoshio Komori , Kevin Burrage
{"title":"Efficient numerical computations for solving high-dimensional stochastic differential equations","authors":"Yoshio Komori ,&nbsp;Kevin Burrage","doi":"10.1016/j.cam.2025.117043","DOIUrl":"10.1016/j.cam.2025.117043","url":null,"abstract":"<div><div>The efficient numerical computations of matrix exponentials in a tensor framework have been recently studied by some researchers. We consider this approach and apply it to exponential methods for stochastic differential equations (SDEs). As a result, we will show that the approach is available for the methods to solve high-dimensional SDEs efficiently.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117043"},"PeriodicalIF":2.6,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145095884","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}
引用次数: 0
Feedback controller design in the frequency domain for high linear n− order systems 高线性n阶系统的频域反馈控制器设计
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-09-10 DOI: 10.1016/j.cam.2025.117052
Guang-Da Hu
{"title":"Feedback controller design in the frequency domain for high linear n− order systems","authors":"Guang-Da Hu","doi":"10.1016/j.cam.2025.117052","DOIUrl":"10.1016/j.cam.2025.117052","url":null,"abstract":"<div><div>We investigate feedback stabilization of linear high-order systems. Using a block matrix expression of the fundamental matrix, stability criteria of the systems are derived. We also present the Fourier transform formulas of the first row in the block matrix expression of the fundamental matrix. Based on the stability criteria and the Fourier transform formulas of the first row, a frequency-domain method is presented to design a stabilizing controller of the systems. We emphasize that all the computations in this paper involve only matrices with lower size. Numerical examples are given to illustrate the main results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117052"},"PeriodicalIF":2.6,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048899","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}
引用次数: 0
Hybrid flux reconstruction schemes with weighted correction functions 带加权校正函数的混合通量重建方案
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-09-10 DOI: 10.1016/j.cam.2025.117046
Lishu Duan , Hanbo Jiang , Shiyi Chen
{"title":"Hybrid flux reconstruction schemes with weighted correction functions","authors":"Lishu Duan ,&nbsp;Hanbo Jiang ,&nbsp;Shiyi Chen","doi":"10.1016/j.cam.2025.117046","DOIUrl":"10.1016/j.cam.2025.117046","url":null,"abstract":"<div><div>This paper proposes a novel approach to developing hybrid flux reconstruction (HFR) schemes through weighted correction functions. The methodology synthesizes correction functions via linear combinations of existing formulations, leading to enhanced numerical properties. The proposed framework is demonstrated by constructing hybrid schemes based on correction functions from the discontinuous Galerkin (DG), spectral difference (SD), and staggered-grid (SG) schemes, representing three well-established classes of FR schemes. Theoretical investigation through von Neumann analysis reveals the influence of weighting parameters on the dissipation and dispersion characteristics. Numerical experiments with the linear advection equation, linearized Euler equations and nonlinear Euler equations demonstrate that optimally weighted correction functions can achieve superior accuracy and stability compared to their constituent base schemes. Specifically, the optimal weighting coefficient in the HFR1 scheme enables it to achieve even higher accuracy than the DG scheme, whereas the optimal weighting coefficient in the HFR2 scheme yields a CFL limit exceeding that of the SG scheme. From a practical perspective, this work provides a straightforward approach for generating a wide range of FR schemes with predictable numerical characteristics.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117046"},"PeriodicalIF":2.6,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046180","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}
引用次数: 0
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