A New Approach for Solving Partial Differential Equations Based on Finite-Difference and Haar Wavelet Methods

Authors

  • Akmal Raza
  • Arshad Khan
  • Khalil Ahmad

Keywords:

Haar wavelet; Finite-difference; Dispersive equation ; Diffusion equation.

Abstract

The main objective of this paper is to develop a new scheme based on finite-difference and Haar wavelet for second order diffusion equation and third order dispersive equation. Further, we have carried out the stability of the Haar wavelet. We solved four problems consisting linear diffusion equation and dispersive homogeneous and non homogeneous equation to validate the developed scheme.
We have also compared our results with existing methods such as finite difference method, global extrapolation method and non polynomial spline method.

Key words and phrases. Haar wavelet; Finite-difference; Dispersive equation ; Diffusion equation.

2010 Mathematics Subject Classification. 65D07; 65M12; 65M99; 65N35; 65N55; 65L10; 65L12

Downloads

Published

2025-05-18

How to Cite

Akmal Raza, Arshad Khan, & Khalil Ahmad. (2025). A New Approach for Solving Partial Differential Equations Based on Finite-Difference and Haar Wavelet Methods. Jordan Journal of Mathematics and Statistics, 14(2), 307–334. Retrieved from https://jjms.yu.edu.jo/index.php/jjms/article/view/811

Issue

Vol. 14 No. 2 (2021)

Section

Articles