Application of Embedded Perturbed Chebyshev Integral Collocation Method for non-linear second-order multi-point boundary value problems.

Abstract

Many problems in theory of elastic stability and kinetic reactions lead to nonlinear multi-point boundary value problems. Therefore in this paper, we present Embedded Perturbed Chebyshev Integral Collocation Method for solving nonlinear second-order multi-point boundary value problems. The approaches in this work are of two-fold: First, we employed Newton-Raphson-Kantorovich linearization procedure to linearise the problems before solving them. Second, we solved the nonlinear systems directly without linearization by Newton’s method to obtain the unknown coefficients. Our investigations showed that the second approach produced better results than Newton-Raphson-Kantorovich linearization approach.