A New Iterative Scheme for the Solution of Tenth Order Boundary Value Problems Using First-Kind Chebychev Polynomials

Abstract

A new iterative scheme for the solution of tenth order boundary value problems has been implemented using first-kind Chebychev polynomials as trial functions. The method involves transforming tenth order boundary value problems into a system of ordinary differential equations (ODEs). The trial solution is introduced into the ODEs, and is evaluated at the boundaries to obtain the approximate solution. The method avoids quasi-linearization, linearization, discretization or perturbation. Also, the method is computationally simple with round-off and truncation errors avoided. Numerical results obtained with the method show that the method is highly reliable and accurate in obtaining the approximate solution of tenth order boundary value problems as compared with the results generated from the Galerkin method available in literature. All computations were performed with maple 18 software.

Keywords: Boundary Value Problem, First-Kind Chebychev Polynomials, Trial solution, Approximate Solution