Techniques for solving integral and differential equations by Legendre wavelets

Abstract

To solve integral and differential equations, this article presents Legendre wavelets method on subintervals. This approach consists of a nonlinear function approximated by Legendre wavelets neural network, computation for Legendre wavelets operational matrix of integration, calculating product operation of Legendre wavelet vector functions and computing integer powers operation of a function approximated by Legendre wavelets. These operators are computed on the subintervals , respectively, and these computations decrease the storage and computational complexity. Using this technique, the integral and differential equations are converted into the solution of system algebraic equations. Numerical experiments demonstrate the validity and applicability of this method.