Important Theories and Applications Arise in Physics and Engineering using a New Technique: The Natural Decomposition Method

Applications of NDM

Abstract

In the current research, we used the natural Adomian decomposition method (NADM), which is a unique technique, to find new exact solutions to partial and ordinary differential equations, such as the Sawada-Kotera equation, the extended fifth-order Korteweg-de Vries (efKdV) equation, and the Caudrey-Dodd-Gibbon equation. We also provided proofs for newly discovered theorems related to natural transformation. Our solutions to both linear and nonlinear differential equations are provided in series form, and the suggested method has high convergence. To handle differential equations, including nonlinear and linear differential equations, the proposed scheme in this work can be simply viewed as an alternative to those found in the literature.