Legendre Wavelets-Picard Iteration Method for Solution of Nonlinear Initial Value Problems

Numerical methods for solving initial value problems (IVPs) are of fundamental importance for analyzing and controlling dynamic systems. In this paper, we first present a new Legendre wavelets-Picard iteration method (LWPIM) for solving IVPs. Combining Legendre wavelets method with Picard iteration method, LWPIM iteratively refines estimates of the solutions until the iteration converges and can avoid the solution of a system of algebraic equations. Furthermore, the developed vector-matrix form makes MCPI methods computationally efficient. Numerical results show that the proposed method is mathematically simple and easy to implement while still keeps the high accuracy