Numerical study of modified Adomianʹs method applied to Burgers equation

The application of Adomianʹs decomposition method to partial differential equations, when the exact solution is not reached, demands the use of truncated series. But the solutionʹs series may have small convergence radius and the truncated series may be inaccurate in many regions. In order to enlarge the convergence domain of the truncated series, Padé approximants (PAs) to the Adomianʹs series solution have been tested and applied to partial and ordinary differential equations, with good results. In this paper, PAs, both in x and t directions, applied to the truncated series solution given by Adomianʹs decomposition technique for Burgers equation, are tested. Numerical and graphical illustrations show that this technique can improve the accuracy and enlarge the domain of convergence of the solution. It is also shown in this paper, that the application of Adomianʹs method to the ordinary differential equations set arising from the discretization of the spatial derivatives by finite differences, the so-called method of lines, may reduce the convergence domain of the solutionʹs series.