ON APPROXIMATE AND CLOSED-FORM SOLUTION METHOD FOR INITIAL-VALUE WAVE-LIKE MODELS

G.O Akinlabi,S.O Edeki

doi:10.12732/ijpam.v107i2.14

Abstract

This work presents a proposed Modified Differential Transform Method (MDTM) for obtaining both closed-form and approximate solutions of initial-value wave-like models with variable, and constant coefficients. Our results when compared with the exact solutions of the associated solved problems, show that the method is simple, effective and reliable. The results are very much in line with their exact forms. The method involves less computational work without neglecting accuracy. We recommend this simple proposed technique for solving both linear and nonlinear partial differential equations (PDEs) in other aspects of pure and applied sciences.

Highlights

Wave equation is a second order Partial Differential Equation (PDE) used in the description of waves
Differential Transform Method (DTM) is an iterative process that is based on the expansion of Taylor series
It was first proposed by Zhou in 1986 when he used it to solve linear and non-linear initial value problems in the analysis of electric circuit [9]

Summary

Introduction

Wave equation is a second order Partial Differential Equation (PDE) used in the description of waves. A variety of numerical, analytical and semianalytical methods have been developed and proposed to obtain approximate, and accurate analytical solutions of various forms of differential equations in literature. Some of these methods include: Homotopy Perturbation Method. DTM is an iterative process that is based on the expansion of Taylor series It was first proposed by Zhou in 1986 when he used it to solve linear and non-linear initial value problems in the analysis of electric circuit [9]. The MDTM is useful in obtaining exact and approximate solutions of linear and non-linear differential systems It has been used by several authors to solve different systems and accurately. The equation (??) is called the modified differential inverse transform of M (x, h) with respect tot

Illustrative and Numerical Examples

Discussion of Results

Concluding Remarks