Approximate Solutions of Coupled Ramani Equation by using RDTM with compared DTM and exact solutions

TL;DR

This paper introduces approximate solutions for the coupled Ramani Equation using RDTM and DTM, demonstrating their effectiveness and efficiency compared to exact solutions.

Contribution

It applies RDTM and DTM to solve the coupled Ramani Equation, highlighting RDTM's simplicity, speed, and better convergence over DTM.

Findings

RDTM provides faster solutions than DTM.

Both methods yield highly accurate results.

RDTM is easier to implement and more convergent.

Abstract

In this paper, we present the new approximate solutions of famous coupled Ramani Equation. In order to obtain the solution, we use the semi-analytic methods differential transform method (DTM) and reduced form of DTM called reduced differential transform method (RDTM). We compare our proposed methods with exact solution and also compare with together. Numerical results show clearly that DTM and RDTM are very effective and also provide very accurate solutions. Additionally, it should be noted that RDTM is applied very easily, fast and more convergent than DTM for these kind of problems.