Numerical solution of nonlinear weakly singular partial integro-differential equation via operational matrices

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• 作者：Somveer Singh^a ; ^{rathaurbhu.90@gmail.com} ; Vijay Kumar Patel^a ; ^{vijaybhuiit@gmail.com} ; Vineet Kumar Singh ; ^a ; ^{vksingh.mat@itbhu.ac.in} ; ^{vks1itbhu@gmail.com} ; Emran Tohidi^b ; ^{emrantohidi@gmail.com}
• 关键词：Singular partial integro-differential equation ; 2D shifted Legendre polynomial ; Operational matrix of differentiation ; Almost operational matrix of integration ; Product operational matrix
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：298
• 期：Complete
• 页码：310-321
• 全文大小：510 K
• 卷排序：298

文摘

In this paper, we propose and analyze an efficient matrix method based on shifted Legendre polynomials for the solution of non-linear volterra singular partial integro-differential equations(PIDEs). The operational matrices of integration, differentiation and product are used to reduce the solution of volterra singular PIDEs to the system of non-linear algebraic equations. Some useful results concerning the convergence and error estimates associated to the suggested scheme are presented. illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.