Analytical solutions of some special nonlinear partial differential equations using Elzaki-Adomian decomposition method

Abstract

We apply the Elzaki-Adomian Decomposition Method (EADM) in this study to solve nonlinear Benjamin-Bona-Mahony (BBM) and Fisher's partial differential equations (PDE). This method, being an integral transform, is a hybrid of two well-known and efficient methods: the Elzaki transform and the Adomian decomposition method. The method is demonstrated by solving two special cases of the BBM Equation and one special case of Fisher's partial differential equation. Because of its high convergence rate in approximating exact solutions, this approach is very dependable. The method can also produce numerical solutions without the usage of restrictive assumptions or the discretization typical of numerical methods; making it free of round-off errors. The Elzaki-Adomian Decomposition method employs a straightforward computation that leads to effectiveness. The efficiency of EADM is demonstrated in the significant reduction of number of numerical computations. The effectiveness and efficiency of EADM account for its broad application, particularly for higher order PDEs.