RBF Based Localized Method for Solving Nonlinear Partial Integro-Differential Equations  

作　　者：Marjan Uddin Najeeb Ullah Syed Inayat Ali Shah 

机构地区：[1]University of Engineering and Technology,Peshawar,Pakistan [2]Islamia College University,Peshawar,Pakistan

出　　处：《Computer Modeling in Engineering & Sciences》2020年第6期957-972,共16页工程与科学中的计算机建模（英文）

摘　　要：In this work,a numerical scheme is constructed for solving nonlinear parabolictype partial-integro differential equations.The proposed numerical scheme is based on radial basis functions which are local in nature like finite difference numerical schemes.The radial basis functions are used to approximate the derivatives involved and the integral is approximated by equal width integration rule.The resultant differentiation matrices are sparse in nature.After spatial approximation using RBF the partial integro-differential equations reduce to the system of ODEs.Then ODEs system can be solved by various types of ODE solvers.The proposed numerical scheme is tested and compared with other methods available in literature for different test problems.The stability and convergence of the present numerical scheme are discussed.

关 键 词：RBFs integral equations local method 

分 类 号：O17[理学—数学]