No abstract

We aim through this paper to present an improved variational iteration method (VIM) based on Bernstein polynomials (BP) approximations to be used with transcendental functions. The key benefits gained from this modification are to reach stable and fairly accurate results and, at the same time, to expand the unknown function’s domain in partial differential equations (PDEs). The proposed approach introduces the Bernstein polynomials in the transcendental functions of nonlinear PDEs. A number of examples were included in order to expound the method’s capacity and reliability. From the results, we conclude that the VIM with BP is a powerful mathematical tool that can be applied to solve nonlinear PDEs.

In this work, a combined technique the Variation Iteration Method (VIM) with the Trapezoidal Rule (TR) was recommend to solve linear and nonlinear fractional ordinary differential equations (F.O.D.E.), where the results obtained from the Variation Iteration method were improved, and numerical results were obtained by determining the maximum absolute errors (MAE) and mean square error (MSE) for the given examples. As the results It is proved that that the proposed method is better than the default method.