A New Approach for Solving Initial Value Problems by Using Modified Energy Balance Method

Abstract

This paper discusses and implements a newly an analytical approach based on Modified Energy Balance Method for solving several mathematical models inspired by applied mathematics that describe the motion of nonlinear oscillations.

After applying the method, we obtain a set of nonlinear algebraic equations, the solution of which requires an iterative method, for determine the initial solution.

In our work, we used one of the modifications of Homotopy Perturbation method, and through this modification we were able to determine the initial solution without using guess the initial solution.

The obtained results improve the exactness and the accuracy of the proposed combinations method is cabable to solve a large number of nonlinear initial value problems.