{"title":"A comprehensive discussion on various methods of generating fractal-like Bézier curves","authors":"Vijay, Gurunathan Saravana Kumar, A. K. B. Chand","doi":"10.1007/s40314-024-02887-0","DOIUrl":"https://doi.org/10.1007/s40314-024-02887-0","url":null,"abstract":"<p>This article explores various techniques for generating fractal-like Bézier curves in both 2D and 3D environments. It delves into methods such as subdivision schemes, Iterated Function System (IFS) theory, perturbation of Bézier curves, and perturbation of Bézier basis functions. The article outlines conditions on subdivision matrices necessary for convergence and demonstrates their use in creating an IFS with an attractor aligned to the convergent point of the subdivision scheme based on specified initial data. Additionally, it discusses conditions for obtaining a one-sided approximation of a given Bézier curve through perturbation. The article also addresses considerations for perturbed Bézier basis functions to construct fractal-like Bézier curves that remain within the convex hull polygon/polyhedron defined by control points. These methods find applications in various fields, including computer graphics, art, and design.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"11 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142178003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A numerical technique for solving singularly perturbed two-point boundary value problems","authors":"Pramod Chakravarthy Podila, Rahul Mishra, Higinio Ramos","doi":"10.1007/s40314-024-02880-7","DOIUrl":"https://doi.org/10.1007/s40314-024-02880-7","url":null,"abstract":"<p>In this article, we first convert a second order singularly perturbed boundary value problem (SPBVP) into a pair of initial value problems, which are solved later using exponential time differencing (ETD) Runge–Kutta methods. The stability analysis of the proposed scheme is addressed. Some linear and non-linear problems have been solved to study the applicability of the proposed method.\u0000</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"3 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chunfeng Cui, Liqun Qi, Guangjing Song, Qing-Wen Wang
{"title":"Moore determinant of dual quaternion Hermitian matrices","authors":"Chunfeng Cui, Liqun Qi, Guangjing Song, Qing-Wen Wang","doi":"10.1007/s40314-024-02884-3","DOIUrl":"https://doi.org/10.1007/s40314-024-02884-3","url":null,"abstract":"<p>In this paper, we extend the Chen and Moore determinants of quaternion Hermitian matrices to dual quaternion Hermitian matrices. We show the Chen determinant of dual quaternion Hermitian matrices is invariant under addition, switching, multiplication, and unitary operations at the both hand sides. We then show the Chen and Moore determinants of dual quaternion Hermitian matrices are equal to each other, and they are also equal to the products of eigenvalues. The characteristic polynomial of a dual quaternion Hermitian matrix is also studied.\u0000</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"24 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Direct and some inverse problems for a generalized diffusion equation with variable coefficients","authors":"Asim Ilyas, S. Malik","doi":"10.1007/s40314-024-02869-2","DOIUrl":"https://doi.org/10.1007/s40314-024-02869-2","url":null,"abstract":"","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"23 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141920482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An inertial extragradient method for solving strongly pseudomonotone equilibrium problems in Hilbert spaces","authors":"Thi Thanh Hai Le, Viet Thong Duong, Tu Vuong Phan","doi":"10.1007/s40314-024-02840-1","DOIUrl":"https://doi.org/10.1007/s40314-024-02840-1","url":null,"abstract":"","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"61 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141922605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An advanced scheme based on artificial intelligence technique for solving nonlinear riccati systems","authors":"Mohd Rashid Admon, N. Senu, A. Ahmadian, Z. Majid","doi":"10.1007/s40314-024-02865-6","DOIUrl":"https://doi.org/10.1007/s40314-024-02865-6","url":null,"abstract":"","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"49 13","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141928190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hojjatollah Shokri Kaveh, Masoud Hajarian, Anthony. T. Chronopoulos
{"title":"Finding solution of linear systems via new forms of BiCG, BiCGstab and CGS algorithms","authors":"Hojjatollah Shokri Kaveh, Masoud Hajarian, Anthony. T. Chronopoulos","doi":"10.1007/s40314-024-02867-4","DOIUrl":"https://doi.org/10.1007/s40314-024-02867-4","url":null,"abstract":"<p>This paper introduces some Krylov subspace methods utilizing the s-step technique. The variable s-step technique is applied to CGS and BiCG algorithms, and extended to the BiCGstab algorithm as an intermediate state between this two algorithms. By proposing the use of the <i>s</i> parameter as a variable, these algorithms become adaptable. To enhance stability, a regularization technique is incorporated. Through the integration of these techniques, stable algorithms are developed. Numerical examples are provided to demonstrate the efficacy and quality of the proposed algorithms.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"13 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Error analysis of the fully Galerkin approximations for the nonlinear extended-Fisher–Kolmogorov equation","authors":"Kaouther Ismail, Ankur, Khaled Omrani","doi":"10.1007/s40314-024-02827-y","DOIUrl":"https://doi.org/10.1007/s40314-024-02827-y","url":null,"abstract":"<p>In this article, we present a fully discrete Crank–Nicolson Galerkin finite element method for solving the two-dimensional nonlinear extended-Fisher–Kolmogorov equation: <span>(u_t + gamma Delta ^2 u -Delta u -u +u^{3} = 0.)</span> The boundedness of the numerical solution in the maximum norm, unique solvability, and related convergence results in <span>(L^2)</span> and <span>(L^{infty })</span>-norms are studied in detail. Also, a new linearized Crank–Nicolson Galerkin modification scheme is designed and error estimate without any time step restrictions is established. Finally, some computational experiments in one and two dimension cases are provided to illustrate the efficacy of our method and to confirm the theoretical results.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"77 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Solving optimal control problems governed by nonlinear PDEs using a multilevel method based on an artificial neural network","authors":"M. Mahmoudi, M. E. Sanaei","doi":"10.1007/s40314-024-02834-z","DOIUrl":"https://doi.org/10.1007/s40314-024-02834-z","url":null,"abstract":"<p>A novel framework is proposed in this research based on multilevel method to solve the optimal control problem. In recent dacades, the mathematical theory of optimal control has rapidly developed into an important and separate field of applied mathematics. The solution of nonlinear partial differential equations is considerably difficult, and the theory of their optimal control is still an open field in many respects. These optimization problems have found diverse applications in various sciences including electrical engineering, mechanical engineering, and aerospace. Current methods for solving this class of optimal control problems usually fall into two classes: discrete-then-optimization or optimization-then-discrete approaches. The proposed approach, however, does not require discretization as it involves rewriting the optimal control problem as a multi-objective optimization problem followed by its solution with a feedforward single-layer artificial neural network based on learning through by the multi-level Levenberg–Marquardt method. Moreover, the convergence of the approach was discussed and some numerical results are presented.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"39 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fateme Amini, Michael A. Henning, Mostafa Tavakoli
{"title":"Local edge metric dimensions via corona products and integer linear programming","authors":"Fateme Amini, Michael A. Henning, Mostafa Tavakoli","doi":"10.1007/s40314-024-02879-0","DOIUrl":"https://doi.org/10.1007/s40314-024-02879-0","url":null,"abstract":"<p>Let <i>G</i> be a connected graph. The distance between two vertices <i>u</i> and <i>v</i> in <i>G</i>, denoted by <span>(d_G(u,v))</span>, is the number of edges in a shortest path from <i>u</i> to <i>v</i>, while the distance between an edge <span>(e = xy)</span> and a vertex <i>v</i> in <i>G</i> is <span>(d_G(e,v) = min {d_G(x,v),d_G(y,v)})</span>. For an edge <span>(e in E(G))</span> and a subset <i>S</i> of <i>V</i>(<i>G</i>), the representation of <i>e</i> with respect to <span>(S={x_1,ldots ,x_k})</span> is the vector <span>(r_G(e|S) =(d_1,ldots ,d_k))</span>, where <span>(d_i=d_G(e,x_i))</span> for <span>(i in [k])</span>. If <span>(r_G(e|S)ne r_G(f|S))</span> for every two adjacent edges <i>e</i> and <i>f</i> of <i>G</i>, then <i>S</i> is called a local edge metric generator for <i>G</i>. The local edge metric dimension of <i>G</i>, denoted by <span>(mathrm{edim_ell }(G))</span>, is the minimum cardinality among all local edge metric generators in <i>G</i>. For two non-trivial graphs <i>G</i> and <i>H</i>, we determine <span>(mathrm{edim_ell }(G diamond H))</span> in the edge corona product <span>(G diamond H)</span> and we determine <span>(mathrm{edim_ell }(Gcirc H))</span> in the corona product <span>(Gdiamond H)</span>. We also formulate the problem of computing <span>(mathrm{edim_ell }(G))</span> as an integer linear programming model.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"10 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}