Equality of partial solutions in the decomposition method for partial differential equations

Abstract

This work considers the partial solutions of partial differential equations for initial/boundary conditions using the Adomian decomposition method. The study formally shows that the partial solutions are always identical for all styles of boundary conditions. We also prove that the partial solution in the t-direction requires less computational work if compared with other partial solutions developed in any space variable direction. In addition, several mathematical models that govern the heat distribution and the wave propagation phenomenas have been tested, and the results obtained have shown that the t-solution minimizes the size of calculations if compared with the traditional techniques.

Keywords:

• Adomian's decomposition method
• partial solutions
• heat equation
• wave equation

C. R. Categories:

• G.1.8