Legendre Wavelets Method for Solving Boundary Value Problems

Abstract

Two techniques for solving n^th order boundary value problem using continuous Legendre wavelets on the interval [0, 1] are presented. The first algorithm solves the boundary value problem BVP directly use the operational matrix of derivative of Legendre wavelets while the second algorithm converts the BVP into a system of Volterra integral equations then using the operational matrix of integration for Legendre wavelets, the system of integral equations is reduced to solve a set of linear algebraic equations, some examples are presented to illustrate the ability of the algorithms.