Journal of Computational and Applied Mathematics最新文献

{"title":"Machine learning to discover discrete fractional chaotic models","authors":"Guo-Cheng Wu ,&nbsp;Zhi-Qiang Wu ,&nbsp;Lianghao Ji","doi":"10.1016/j.cam.2025.116869","DOIUrl":"10.1016/j.cam.2025.116869","url":null,"abstract":"<div><div>This paper suggests machine learning for discrete fractional modeling. First, a multi-layer neural network is established, and the loss function is constructed using a physics-informed neural network. Then, the Adam algorithm is used to train neural networks and solve the discretization optimization problem of weights and sparse vectors. Compensate and incommensurate fractional chaotic systems are demonstrated to show the efficiency, respectively. This paper provides a machine learning method to accurately capture long interactions in nonlinear phenomena and directly establish discrete fractional chaotic systems from observed data.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"473 ","pages":"Article 116869"},"PeriodicalIF":2.1,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144535615","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}

{"title":"Comprehensive closed-form analysis of bifurcation in inductive wireless power transfer systems","authors":"Seyit A. Sis","doi":"10.1016/j.cam.2025.116847","DOIUrl":"10.1016/j.cam.2025.116847","url":null,"abstract":"&lt;div&gt;&lt;div&gt;An inductive wireless power transfer (IWPT) system utilizing common compensation topologies-series (SS), series–parallel (SP), parallel–series (PS), and parallel–parallel (PP)-forms a coupled resonant system that exhibits either a single &lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt; or three zero phase angle (ZPA) frequencies (&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;), depending on the load and coupling conditions. The bifurcation phenomenon in such systems refers to the conditional emergence of two additional ZPA frequencies ( &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; ) near the inherently present ZPA frequency &lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt;, leading to a total of those three ZPA frequencies. Exact closed-form expressions for the bifurcation criteria, the inherent ZPA frequency &lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt;, as well as the reflected resistance and reactance at &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, have been extensively studied and are well-established for all four compensation topologies. However, precise closed-form solutions for these parameters at the conditionally emerging ZPA frequencies ( &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt; remain incomplete.&lt;/div&gt;&lt;div&gt;In order to derive the missing closed-form solutions at the ZPA frequencies, this paper reexamines four common compensation topologies in inductive wireless power transfer (IWPT) systems. A circuit model based on mutual inductance is analyzed to establish the necessary equations for the solutions. The primary contribution of this work is to present closed-form expressions for the previously unavailable parameters at &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. In this context &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; are formulated as functions of the circuit model parameters for all four compensation topologies. Additionally, closed-form expressions for the input resistance ( &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"473 ","pages":"Article 116847"},"PeriodicalIF":2.1,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490158","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}

{"title":"Convergence analysis of a novel Strang directional splitting method for the Allen–Cahn equations","authors":"Min Gao ,&nbsp;Chaoyu Quan ,&nbsp;Zhen Zhang","doi":"10.1016/j.cam.2025.116868","DOIUrl":"10.1016/j.cam.2025.116868","url":null,"abstract":"<div><div>High performance computing has attracted more attention in modern study of scientific computing. In this paper, we propose an unconditionally energy stable numerical scheme for the Allen–Cahn equation which is second-order accurate in both space and time. The scheme employs the alternating-direction implicit (ADI) splitting to decouple the computation of spatial derivatives and the Strang splitting to decouple the computation of the nonlinear term from the linear one. The decoupling in spatial dimensions and nonlinear terms allows easy implementations of high performance computing techniques. The resulting schemes, which we call the Strang directional splitting (SDS) schemes, are rigorously shown to enjoy the unconditional energy stability for a modified energy and the second-order accuracy in both space and time. The SDS method is further generalized to numerically solve variable-coefficient Allen–Cahn equations in arbitrarily high dimensions, where the unconditional energy stability is still ensured. Its numerical efficiency is demonstrated through extensive simulation results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"473 ","pages":"Article 116868"},"PeriodicalIF":2.1,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144501705","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}

{"title":"Improved approximation via hybrid Shepard–Lagrange operators: Linear and nonlinear perspectives","authors":"Oktay Duman","doi":"10.1016/j.cam.2025.116864","DOIUrl":"10.1016/j.cam.2025.116864","url":null,"abstract":"<div><div>This paper introduces a hybrid operator that combines Shepard operators with Lagrange polynomials, proving that the new operator exhibits superior approximation properties compared to the classical Shepard operator. In the linear case, our approach advances known results in the literature, providing a more effective framework for approximation. Building on this foundation, the method is also extended to nonlinear scenarios by employing max-product operations, demonstrating that the nonlinear operator achieves even better approximation characteristics than its linear counterpart. The theoretical findings are validated through numerical computations and graphical representations, strongly supporting the effectiveness of the hybrid operator in both linear and nonlinear contexts.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"473 ","pages":"Article 116864"},"PeriodicalIF":2.1,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144501704","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}

{"title":"The exact region determined by Blomqvist’s beta, Spearman’s footrule and Gini’s gamma","authors":"Damjana Kokol Bukovšek,&nbsp;Blaž Mojškerc","doi":"10.1016/j.cam.2025.116861","DOIUrl":"10.1016/j.cam.2025.116861","url":null,"abstract":"<div><div>To quantify the degree of association between random variables, concordance measures are employed. To express such a degree, a single measure might give too much space, so several are used for comparison. In this paper we study the ternary relation between three well-known (weak) concordance measures, namely Blomqvist’s beta, Spearman’s footrule and Gini’s gamma. In other words, given the values of Blomqvist’s beta and Spearman’s footrule, we determine the degree of freedom a copula has at taking the value of Gini’s gamma. We explicitly determine the 3-dimensional region representing the relation. We also provide copulas where bounds of the region are attained.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"473 ","pages":"Article 116861"},"PeriodicalIF":2.1,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490299","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}

{"title":"The ∂̄-dressing method, Bäcklund transformation and exact solutions for a (3+1)-dimensional generalized Ito equation","authors":"Zhenbo Wang ,&nbsp;Yufeng Zhang ,&nbsp;Yanmei Sun","doi":"10.1016/j.cam.2025.116817","DOIUrl":"10.1016/j.cam.2025.116817","url":null,"abstract":"<div><div>In this paper, we present an improved version of the <span><math><mover><mrow><mi>∂</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span>-dressing method and apply it to the (3+1)-dimensional generalized Ito (3D-gIto) equation, successfully constructing new classes of exact solutions. These exact solutions include functional parameters solutions, kink solitons, bright–dark breather waves, breather lump-type solutions, bright–dark solitons, and lump-type solitons. Notably, we show that these solutions, both real and complex, exhibit distinct characteristics such as boundedness, singularity, and non-singularity. Our improved <span><math><mover><mrow><mi>∂</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span>-dressing method has not only made significant progress in solving the 3D-gIto equation but also provided ideas for solving other (3 +1)-dimensional integrable equations. Furthermore, we derive the B<span><math><mover><mrow><mi>a</mi></mrow><mrow><mo>̈</mo></mrow></mover></math></span>cklund transformation for 3D-gIto equation, yielding various solutions, including kink solitons, anti-kink solitons, breather waves, singular bright–dark breather waves.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"473 ","pages":"Article 116817"},"PeriodicalIF":2.1,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144480621","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}

{"title":"Acceleration of implicit schemes for large systems of delay differential equations","authors":"Mouhamad Al Sayed Ali ,&nbsp;Miloud Sadkane","doi":"10.1016/j.cam.2025.116863","DOIUrl":"10.1016/j.cam.2025.116863","url":null,"abstract":"<div><div>The objective is to accelerate numerical implicit schemes for solving large linear or nonlinear delay differential equations. These schemes require solving large linear or nonlinear systems at each integration step, making effective initial guesses critical for rapid convergence. For nonlinear problems, an inexact Newton method is used, whose efficiency depends heavily on the quality of these initial guesses. To generate them, line search or trust-region algorithms are employed-each involving the solution of large linear systems. These linear systems are solved using a Krylov subspace method. Initial guesses are constructed via a Petrov–Galerkin process applied to low-dimensional approximation subspaces derived from previous steps. Error estimates are provided, linking the accuracy of the initial guesses to the timestep size, the scheme’s order, and the subspace dimension. Numerical experiments show speedups of up to two orders of magnitude over standard predictor-based methods, when those converge.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"473 ","pages":"Article 116863"},"PeriodicalIF":2.1,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490298","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}

{"title":"Weakly robust global optimization of max-plus linear systems with non-negative constraint sets and its application to optimizing time parameters in data transmission systems","authors":"Weili Yang,&nbsp;Yuegang Tao,&nbsp;Weipeng Liu","doi":"10.1016/j.cam.2025.116855","DOIUrl":"10.1016/j.cam.2025.116855","url":null,"abstract":"<div><div>This paper considers the weakly robust global optimization problem of max-plus linear systems with non-negative constraint sets. A characteristic of the weak robustness of global optimization is given, and the weakly robust perturbation bound is constructed to ensure that the parameter perturbations within the bound do not affect the original global minimum and one globally optimal solution. The maximal element of each row in a max-plus matrix is used to characterize the variable elements and invariable elements, and their maximum number is determined. The relatively maximal perturbation bounds are derived by using all variable and invariable elements, and a polynomial algorithm for finding these bounds is provided. The proposed weakly robust global optimization is applied to optimizing time parameters in data transmission systems. The effectiveness of the proposed method is demonstrated by examples.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"473 ","pages":"Article 116855"},"PeriodicalIF":2.1,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144480620","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}

{"title":"Stability analysis and numerical solution of fourth-order neutral Volterra integro-differential equation","authors":"Burcu Fedakar ,&nbsp;Ilhame Amirali ,&nbsp;Gabil M. Amiraliyev","doi":"10.1016/j.cam.2025.116850","DOIUrl":"10.1016/j.cam.2025.116850","url":null,"abstract":"<div><div>In this paper, we study an initial-value problem for a fourth-order neutral Volterra integro-differential equation. First, the properties of the exact solution are analysed. Next, the problem is solved numerically using the finite difference method containing the composite trapezoidal rule for the integral part of the equation. Error estimate for the approximate solution is carried out and second-order convergence is attained. In support of the idea, numerical examples are given.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"473 ","pages":"Article 116850"},"PeriodicalIF":2.1,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632725","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}

{"title":"An auto-stabilized weak Galerkin method for elasticity interface problems on nonconvex meshes","authors":"Chunmei Wang ,&nbsp;Shangyou Zhang","doi":"10.1016/j.cam.2025.116854","DOIUrl":"10.1016/j.cam.2025.116854","url":null,"abstract":"<div><div>This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for elasticity interface problems on general polygonal and polyhedral meshes, without requiring convexity constraints. The method utilizes bubble functions as key analytical tools, eliminating the need for stabilizers typically used in traditional WG methods and leading to a more streamlined formulation. The proposed method is symmetric, positive definite, and easy to implement. Optimal-order error estimates are derived for the WG approximations in the discrete <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm, assuming the exact solution has sufficient smoothness. Numerical experiments validate the accuracy and efficiency of the auto-stabilized WG method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"473 ","pages":"Article 116854"},"PeriodicalIF":2.1,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144471946","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}