The Cauchy Problem for Nonlinear Higher Order Partial Differential Equations Using Projected Differential Transform Method

  • H. O. Orapine hycienthorapine@naub.edu.ng
  • A. A. Baidu Department of Mathematics, Faculty of Natural and Applied Sciences, Nigerian Army University Biu, Borno State, Nigeria
  • I. M. Kwaghkor Department of Mathematics, Faculty of Natural and Applied Sciences, Nigerian Army University Biu, Borno State, Nigeria
Keywords: Cauchy problem, Nonlinear Higher Order Partial Differential equation, Hyperbolic Equation, Wave-like Equation

Abstract

This study applies the Projected Differential Transform Method (PDTM) to solve nonlinear higher-order partial differential equations (PDEs). The Projected Differential Transform (PDT) series solutions converge to exact solutions with relative ease. Numerical problems of fourth- and sixth-order nonlinear hyperbolic equations and nonlinear wave-like equations with variable coefficients are solved to show that PDTM can efficiently provide exact solutions for nonlinear PDEs of higher order with initial conditions. The results demonstrate that the PDTM is exceptionally accurate, efficient, and reliable and that it can be applied to many other types of nonlinear higher-order PDEs. Compared to the Modified Decomposition Method, the Homotopy Analysis Approach, and the Homotopy Perturbation Method, this method significantly reduces numerical computations and outperforms in accuracy

Published
2023-11-30
How to Cite
Orapine, H. O., Baidu, A. A., & Kwaghkor, I. M. (2023). The Cauchy Problem for Nonlinear Higher Order Partial Differential Equations Using Projected Differential Transform Method. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 9(2), 74 - 89. Retrieved from http://ijmso.unilag.edu.ng/article/view/1981
Issue
Vol 9 No 2 (2023)
Section
Articles

Copyright (c) 2023 H. O. Orapine, A. A. Baidu, I. M. Kwaghkor

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, adaptation, and reproduction in any medium, provided that the original work is properly cited.