Legendre approximation solution for a class of higher-order Volterra integro-differential equations

The aim of this work is to study the Legendre wavelets for the solution of boundary value problems for a class of higher order Volterra integro-differential equations using function approximation. The properties of Legendre wavelets together with the Gaussian integration method are used to reduce the problem to the solution of nonlinear algebraic equations. Also a reliable approach for convergence of the Legendre wavelet method when applied to a class of nonlinear Volterra equations is discussed. Illustrative examples have been discussed to demonstrate the validity and applicability of the technique and the results obtained by Legendre wavelet method is very nearest to the exact solution. The results demonstrate reliability and efficiency of the proposed method.