Approximate solution method for third-order multi-point boundary value problems

Abstract

In this paper, we formulate a method using Chebyshev polynomials for solving both linear and non-linear multi-point boundary value problems. Quasi linearization technique is used to transform a non-linear boundary value problem into a sequence of linear boundary value problems with a quadratic polynomial which satisfies the boundary conditions chosen as the initial approximation. Four numerical examples are given to demonstrate the efficiency of the present method and the results obtained are compared with other methods in the literatures.