Method based on quasi variable mesh for solution of system of second order boundary value problems with mixed boundary conditions

Abstract

A new numerical method with third order accuracy is presented for the solution of nonlinear two point boundary value problems(BVPs) with mixed boundary conditions using quasi variable mesh. In case of uniform mesh, method becomes fourth order. The method has been extended to vector form. Error analysis of the proposed scheme using a model problem is discussed. Application to fourth order nonlinear boundary value problem in coupled form is discussed. The proposed method is tested on two examples of linear and nonlinear BVPs and comparison with uniform mesh method has been made to prove the accuracy of the method.