A new approximation method to solve boundary value problems by using functional perturbation concepts

Abstract

Functional perturbation method (FPM) is presented for the solution of differential equations with boundary conditions. Some properties of FPM are utilized to reduce the differential equation with variable coefficients to the equations with constant coefficients. The FPM can be applied directly for many types of differential equations. The exact solution is obtained by only the first term of the Frechet series for polynomial cases. Four examples are included to demonstrate the method.