Power Series Solution for Solving Nonlinear Burgers-Type Equations

Eduardo López-Sandoval ,A R Samana,Juan José Godina-Nava ,Alexandre Mello

doi:10.1155/2015/712584

Abstract

Power series solution method has been traditionally used to solve ordinary and partial linear differential equations. However, despite their usefulness the application of this method has been limited to this particular kind of equations. In this work we use the method of power series to solve nonlinear partial differential equations. The method is applied to solve three versions of nonlinear time-dependent Burgers-type differential equations in order to demonstrate its scope and applicability.

Highlights

Power series solution (PSS) method is an old method that has been limited to solve linear differential equations, both ordinary differential equations (ODE) [1, 2] and partial differential equations (PDE) [3, 4]
In this work we have shown that it is possible to solve nonlinear differential equations with the power series solution method
This method is implemented as a general approximate solution for each nonlinear PDE or ODE, in a similar way to the solution of a Linear DE

Summary

Introduction

Power series solution (PSS) method is an old method that has been limited to solve linear differential equations, both ordinary differential equations (ODE) [1, 2] and partial differential equations (PDE) [3, 4]. Linear PDE have traditionally been solved using the separation of variables method because it permits obtaining a coupled system of ODE easier to solve with the PSS method Some examples of these are the Legendre polynomials and the spherical harmonics used in Laplace’s equations in spherical coordinates or in Bessel’s equations in cylindrical coordinates [3, 4]. The SM with collocation points (SMCP) is a numerical technique applied to solve linear and nonlinear differential equations with high accurate approximations to the solution [6] This has been used to solve PDE using polynomial interpolation function with an orthogonal basis such as Fourier, Chebyshev, or Legendre functions [7]. This program helps to do easier the tedious algebraic operations

Power Series Solution Method

Numerical Results

Discussion and Conclusions