Adapting partial differential equations via the modified double ARA-Sumudu decomposition method

In order to get analytical series solutions of partial differential equations while taking certain conditions into consideration, this paper presents the new procedure of using the new double ARA-Sumudu transform (DARA-ST) in conjunction with the modified decomposition method in handling nonlinear equations. The solutions of the nonlinear terms in these equations are obtained depending on defining series of iterations. The suggested method has the merits of producing accurate answers and it is simply analytically applicable to the provided problems. Moreover, fundamental theorems and properties of DARA-ST are proposed. Numerical examples are provided to show how this strategy might be used and how beneficial it is. The obtained results demonstrate the method’s potential for resolving further nonlinear problems and getting exact solutions.