Haar Wavelet Method for the Solution of Sixth-Order Boundary Value Problems

Abstract

In this article, a numerical scheme is developed for the solution of sixth-order boundary value problems (BVP). The Haar collocation method is developed for both linear and nonlinear boundary value problems. In this method, the sixth-order derivative in boundary value problem is approximated using Haar functions, and integration is used to obtain the values of lower derivatives and approximate solution. Some examples are given for the convergence of the proposed method. The Haar technique devoted in this paper is compared with Septic spline method, Sine–Galerkin method, and decomposition method. Maximum absolute and root-mean-square errors are given for different Gauss and collocation points (CPs). Convergence rate using distinct numbers of nodal points is calculated, which is nearly equal to 2.