Power Series Extender Method for the Solution of Nonlinear Differential Equations

Abstract EN

We propose a power series extender method to obtain approximate solutionsof nonlinear differential equations.

In order to assess the benefits of this proposal, three nonlinearproblems of different kind are solved and compared against the power series solution obtained usingan approximative method.

The problems are homogeneous Lane-Emden equation of α index, governingequation of a burning iron particle, and an explicit differential-algebraic equation related to batterymodel simulations.

The results show that PSEM generates highly accurate handy approximationsrequiring only a few steps.

The main advantage of PSEM is to extend the domain of convergence ofthe power series solutions of approximative methods as Taylor series method, homotopy perturbationmethod, homotopy analysis method, variational iteration method, differential transform method, and Adomiandecomposition method, among many others.

From the application of PSEM, it results in handy easycomputable expressions that extend the domain of convergence of high order power series solutions.