Integro perturbation method for ordinary differential equations

Abstract

A new analytical solution method is proposed for ordinary differential equations. Starting with an initial perturbation solution, a first iteration solution is obtained by directly integrating the highest order term while substituting the assumed perturbed solution to the remaining terms. The iterations can be repeated to obtain a satisfactory converged solution in the domain of interest. The method has been applied to four sample first and second order linear and nonlinear differential equations. The iteration solutions are contrasted with the available exact solutions. The method is simple, straightforward and converges to the real solution if the initial perturbation solution is a good starting assumption.