Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations

This paper develops amodified variational iterationmethod coupled with the Legendre wavelets, which can be used for the efficient numerical solution of nonlinear partial differential equations (PDEs).The approximate solutions of PDEs are calculated in the form of a serieswhose components are computed by applying a recursive relation. Block pulse functions are used to calculate the Legendre wavelets coefficientmatrices of the nonlinear terms.Themain advantage of the newmethod is that it can avoid solving the nonlinear algebraic system and symbolic computation. Furthermore, the developed vector-matrix form makes it computationally efficient. The results show that the proposed method is very effective and easy to implement.