A Haar Wavelets Based Numerical Method for Third-order Boundary and Initial Value Problems

Abstract

Uniform Haar wavelets method is proposed to find approximate solution of multi-point third-order boundary-value problems (BVPs) related to flow in a wedge-shaped region, sandwich beam model, system of ordinary differential equations, nonlinear third-order Initial-value Problems (IVPs) in thin film flow. The distinctive feature of the present method is that it can be used to find numerical solution of both BVPs and IVPs without transformation of BVPs into IVPs or vice versa (1). Performance of the Haar wavelets is compared with the finite difference method, Pade approximant, spline based methods, method of superposition, method of chasing and method of adjoint operators. More accurate solutions can be obtained by increasing the level in the Haar wavelet. The main advantage of this method is its efficiency and simple applicability. Convergence analysis of the proposed method alongside numerical procedure for multi-point BVPs and IVPs are given to test accuracy of the method.