Jacobi operational matrix and its application for solving systems of ODEs (Q347100)

The paper is concerned with the computation of the Jacobi operational matrix of differentiation and its applications. Jacobi polynomials and their approximation properties are reviewed and the method for the computation of Jacobi operational matrix is proposed. The tau method using the shifted Jacobi polynomials is used for solving the systems of linear ordinary differential equations (ODEs) subject to the initial or boundary conditions. The systems of nonlinear ordinary differential equations are solved by a collocation method using Jacobi polynomials and their zeros as collocation points. Four illustrative numerical examples are presented.