Bernstein-Chebyshev integral collocation method for solving third-order multi-point boundary value problems.

Abstract

In this paper, combination of Bernstein and Chebyshev approximations are developed and adopted for the numerical solution of third-order linear and nonlinear multi-point boundary value problems. The whole idea of the method is based on the Bernstein-Chebyshev approximation for the third-order derivatives and we generate approximations to the second-order, first-order and function y itself through successive integration of third-order derivative. Newton’s linearization scheme is employed to linearize the nonlinear equations and then resulting to iterative procedure. Numerical examples of linear and nonlinear problems are considered to illustrate the efficiency and reliability of the method and the results obtained are compared with other methods in the literature.