Abstract

In this paper, we present a modified and new version of spectral method which is based on minimization of obtained residual term in  norm, where  is a weight function with respect to Jacobi polynomials. Using this approach is efficient and effective rather than Tau and collocation methods. It reduces the nonlinear ordinary differential equations to the nonlinear programming problems which is an easy problem to solve. Hence, easy implementation of the method is the importance of our approach and some numerical test experiments show the accuracy and efficiency of this method.

Key words: A new spectral method, nonlinear ordinary differential equations.