Theoretical analysis of new techniques applied to applications in fluid dynamics

Abstract

ABSTRACT In this research study, we explore new proofs of theorems related to a novel technique by the name of the natural Adomian decomposition method (NADM), and then we apply it to find new exact solutions to nonlinear partial differential equations under proper initial conditions. Our solutions to nonlinear differential equations are given in series format, with convergence analysis for the proposed scheme. The new approach in this work can be considered as an alternative technique for the ones in the literature, to handle KdV-type equations such as the fifth-order Korteweg–de Vries (efKdV) equation, which is a crucial equation in fluid dynamics for the description of nonlinear wave processes. The new technique is a novel one to treat applications in the fields of mathematics, biology, engineering, physics, and other areas of science.