Application of the Triple Sumudu Decomposition Method for Solving 1+1 and 2+1-Dimensional Boussinesq Equations

Abstract

The triple Sumudu transform decomposition method (TSTDM) is a combination of the Adomian decomposition method (ADM) and the triple Sumudu transform. It is a computational method that can be appropriate for solving linear and nonlinear partial differential equations. The existence analysis of the method and partial derivatives theorems are proven. Finally, we solve the 1+1 and 2+1-dimensional Boussinesq equations by applying the (TSTDM)technique, which gives the approximate solution with quick convergence. It is more precise than using ADM alone. In addition, three examples are offered to examine the performance and precision of our method.