The Revised NIM for Solving the Non-Linear System Variant Boussinesq Equations and Comparison with NIM

Abstract

This research aims to guide researchers to use a new method, and it is the Revised New Iterative Method (RNIM) to solve partial differential equation systems and apply them to solve problems in various disciplines such as chemistry, physics, engineering and medicine. In this paper, the numerical solutions of the nonlinear Variable Boussinesq Equation System (VBE) were obtained using a new modified iterative method (RNIM); this was planned by (Bhaleker and Datterder-Gejj). A numerical solution to the Variable Boussinesq Equation System (VBE) was also found using a widely known method, a new iterative method (NIM). By comparing the numerical solutions of RNIM and NIM methods, the solution VBE using the new revised iterative process (RNIM), is accurate, reliable, robust, promising and quickly arrives at the exact solution. Moreover, the results also show that the solution of the (RNIM) is more reliable and faster compared to the new iterative method. Finally, a solution by RNIM is easy to calculate, but sometimes requires more calculations.