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A comprehensive discussion on various methods of generating fractal-like Bézier curves 全面探讨生成分形贝塞尔曲线的各种方法
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-12 DOI: 10.1007/s40314-024-02887-0
Vijay, Gurunathan Saravana Kumar, A. K. B. Chand
{"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}
引用次数: 0
A numerical technique for solving singularly perturbed two-point boundary value problems 解决奇异扰动两点边界值问题的数值技术
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-11 DOI: 10.1007/s40314-024-02880-7
Pramod Chakravarthy Podila, Rahul Mishra, Higinio Ramos
{"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}
引用次数: 0
Moore determinant of dual quaternion Hermitian matrices 双四元赫米矩阵的摩尔行列式
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-10 DOI: 10.1007/s40314-024-02884-3
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}
引用次数: 0
Direct and some inverse problems for a generalized diffusion equation with variable coefficients 具有可变系数的广义扩散方程的直接问题和一些反问题
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-10 DOI: 10.1007/s40314-024-02869-2
Asim Ilyas, S. Malik
{"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}
引用次数: 0
An inertial extragradient method for solving strongly pseudomonotone equilibrium problems in Hilbert spaces 求解希尔伯特空间强伪单调平衡问题的惯性外梯度法
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-09 DOI: 10.1007/s40314-024-02840-1
Thi Thanh Hai Le, Viet Thong Duong, Tu Vuong Phan
{"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}
引用次数: 0
An advanced scheme based on artificial intelligence technique for solving nonlinear riccati systems 基于人工智能技术的非线性里卡提系统高级求解方案
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-08 DOI: 10.1007/s40314-024-02865-6
Mohd Rashid Admon, N. Senu, A. Ahmadian, Z. Majid
{"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}
引用次数: 0
Finding solution of linear systems via new forms of BiCG, BiCGstab and CGS algorithms 通过新形式的 BiCG、BiCGstab 和 CGS 算法寻找线性系统的解决方案
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-07 DOI: 10.1007/s40314-024-02867-4
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}
引用次数: 0
Error analysis of the fully Galerkin approximations for the nonlinear extended-Fisher–Kolmogorov equation 非线性扩展渔-科尔莫哥罗夫方程的全伽勒金近似的误差分析
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-07 DOI: 10.1007/s40314-024-02827-y
Kaouther Ismail, Ankur, Khaled Omrani
{"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}
引用次数: 0
Solving optimal control problems governed by nonlinear PDEs using a multilevel method based on an artificial neural network 使用基于人工神经网络的多层次方法解决非线性 PDE 所控制的优化控制问题
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-06 DOI: 10.1007/s40314-024-02834-z
M. Mahmoudi, M. E. Sanaei
{"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}
引用次数: 0
Local edge metric dimensions via corona products and integer linear programming 通过日冕积和整数线性规划实现局部边缘度量维度
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-04 DOI: 10.1007/s40314-024-02879-0
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}
引用次数: 0
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