Efficient approach for solving high order (2+1)D-differential equation

This article presents an exact analysis solution for high order (2+1) dimensional differential equations by using an efficient approach based on coupled method via LA-transform with decomposition method to overcome the computational difficulties. Convergence of series solution has been discussed with two illustrated examples, and the method has shown a high-precision, fast approach to solve non-linear (2+1) dimensional PDEs with initial condition. There is no need of any discretization of domain or assumption for a small parameter to be present in the problem. The steps of the suggested method are easily implemented. High accuracy and a rapid convergence to the exact solution compared with other methods can be used to solve types of PDEs.