On solving ordinary differential equations of the first order by updating the Lagrange multiplier in variational iteration ‎method

Abstract

In this paper, we have proposed a new iterative method for finding the solution of ordinary differential equations of the first order. In this method we have extended the idea of variational iteration method by changing the general Lagrange multiplier which is defined in the context of the variational iteration method.This causes the convergent rate of the method increased compared with the variational iteration method. To prevent consuming large amount of the CPU time and computer memory and to control requires significant amounts of computations, the Taylor expansion of the iterative functions in each iteration are applied. Finally to extend the convergence region of the truncated series, also the Pade approximants are used. Error analysis and convergence of the method are studied. Some examples are given to illustrate the performance and efficiency of the proposed method. For comparison, the results obtained by the our method and the variational iteration method are ‎presented.