Shifted Jacobi Collocation Method Based on Operational Matrix for Solving the Systems of Fredholm and Volterra Integral Equations

[摘要] This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product. The main aim is to generalize the Jacobi integralandproductoperationalmatricestothesolvingsystemofFredholmand Volterra equations. These matrices together with the collocation method are applied to reduce the solution of these problems to the solution of a system of algebraic equations. The method is applied to solve system of linear and nonlinear Fredholm and Volterra equations. Illustrative examples are included to demonstrate the validity and efficiency of the presented method. Also, several theorems, which are related to the convergence of the proposed method, will be presented.

[学科分类] 计算数学

[关键词] Collocation Method;Shifted Jacobi Polynomials;System of Fredholm;Volterra Integral Equations;Convergence;Operational Integral;Product Matrices