Numerical Solutions of Time Dependent Partial Differential Equations via HAAR Wavelets

Authors

  • Abdul Ghafoor Department of Mathematics, Kohat University of Science & Technology (KUST), Kohat, Pakistan.

DOI:

https://doi.org/10.47264/idea.nasij/1.1.4

Keywords:

Wavelets, Finite Difference, Burgers’ Equation, Boussinesq Equation

Abstract

An effective wavelet based scheme coupled with finite difference is used for the solution of two nonlinear time dependent problems namely: Burgers' and Boussinesq equations. These equations have wide-spread application in many fields such as viscous medium, turbulence , uid dynamics, infiltration phenomena etc. The proposed scheme convert the partial differential equations (PDE) to system of algebraic equations. The obtained system can be solved easily. In this paper convergence of the scheme is also discussed to show validity of the technique. Effectiveness of the scheme is shown with the help of test problems. Numerical results verify that the suggested scheme is more accurate, convenient, fast and require low computational cost.

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Published

2020-12-31

How to Cite

Ghafoor, A. (2020). Numerical Solutions of Time Dependent Partial Differential Equations via HAAR Wavelets. Natural and Applied Sciences International Journal (NASIJ), 1(1), 39–52. https://doi.org/10.47264/idea.nasij/1.1.4

Issue

Vol. 1 No. 1 (2020): January-December 2020

Section

Research Articles

Categories

License

Copyright (c) 2020 Abdul Ghafoor

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