Transformed Generate Approximation method for generalized boundary value problems using first-kind Chebychev polynomials

Abstract

In this paper, a new numerical method, the Transformed Generate Approximation Method (TGAM) is proposed for generalized boundary value problems with first-kind Chebychev polynomials as trial functions. In this method, the trial functions are substituted into the transformed system of ordinary differential equations in order to generate systems of linear algebraic equations satisfying the boundary conditions, which on solving yield the required approximate solution. The method is structurally simple as it requires no perturbation or discretization. The method is reliable in seeking the solution of boundary value problems as numerical illustrations reveal. Results obtained were compared with the exact solution and other methods available in literature. Also, convergence analysis of the method is presented. All computations are carried out with Maple 18 software.

Keywords: Boundary value problem, Chebychev polynomials, Trial functions, Approximate solution