A new acceleration of variational iteration method for initial value problems

This paper is devoted to accelerating the variational iteration method (VIM) to solve a nonlinear initial value problem. For this purpose, the redundant calculations of the conventional VIM are removed, and the complex integration is evaluated recursively and quickly with a suitable numerical approximation. The convergence of the proposed method is proven, and an efficient implementation algorithm is presented. This method is successfully applied to solve three applied equations, including the Riccati equation, the Lane-Emden equation, and the SIR epidemic model with a constant vaccination rate. Numerical simulations show that this improvement has significantly increased the method's speed and enlarged its convergence region. & COPY; 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.