The agreement between novel exact and numerical solutions of nonlinear models

Abstract

Nonlinear models (NLMs), being an important topic in mathematical physics, have attracted a lot of attention in the international research community because they have numerous uses in human life. These NLMs are typically implemented to illuminate various complicated natural phenomena. NLMs have been seen in fluid mechanics, optical physics, signal processing, plasma physics, acoustic waves, traffic flow, atomic physics, mathematical physics, nuclear energy, and other applications. That's why we consider the Mikhailov-Novikov-Wang (M-N-W) integrable equation. In this project, we acquire exact solutions (ESs) and numerical solutions (NSs) of the M-N-W integrable equation. Primarily, we use the modified (G′/G)-expansion method (MDG/GEM) and adomian decomposition method (ADM) to find new ESs and NSs of the M-N-W integrable equation. This present project work is mainly concentrated on finding new ESs and NSs for a broad class of the M-N-W integrable equation using the MDG/GEM and ADM, respectively, and making a comparison between these two kinds of solutions. Additionally, using recent scientific instruments, the two-dimensional, three-dimensional, and contour plots are displayed, as well as comparison plots between graphs of analytical and numerical solutions of the M-N-W integrable equation. NLMs have appeared in a wide variety of engineering, physics, and applied mathematics; hence, it is natural to expect that this project should have broad applicability.