Taylor series for the Adomian decomposition method

Abstract

In this paper, we analyse the exact solutions to scalar partial differential equations obtained, thanks to the summable Taylor series provided by Adomian's decomposition method. We propose a modification of the method which makes the calculations of Taylor coefficients easier and more direct. The difference is essential, for instance, in the case of non-homogenous equations or initial conditions and is illustrated by some examples.

Keywords:

• Adomian decomposition method
• exact solutions
• Taylor series

2010 AMS Subject Classifications :

• 35C10
• 35C05
• 65D15

Acknowledgements

I am in debt to Professor Randolph Rach for all the advice, comments and recommended papers, as well as for access to some of them. The presented research was partially supported by the Polish Ministry of Science and Higher Education.