Solving Three Dimensional and Time Depending PDEs by Haar Wavelets Method - Open Access Library Journal

OALibJ > Vol.5 No.5, May 2018

Solving Three Dimensional and Time Depending PDEs by Haar Wavelets Method ()

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DOI: 10.4236/oalib.1104496 739 Downloads 2,356 Views Citations

Author(s)

Abdeljalil Nachaoui¹, Ekhlass S. Al-Rawi², Ahmed F. Qasim²

Affiliation(s)

¹Jean Leary Laboratory of Mathematics, University of Nantes, Nantes, France.
²College of Computer Sciences and Mathematics, University of Mosul, Mosul, Republic of Iraq.

ABSTRACT

Haar wavelets are applied for solution of three dimensional partial differential equations (PDEs) or time depending two dimensional PDEs. The proposed method is mathematically simple and fast. Two techniques are used in numerical solution, the first based on 2D-Haar wavelets and the second based on 3D-Haar wavelets and we compare them. To demonstrate the efficiency of the method, two test problems (solution of the diffusion and Poisson equations) are discussed. Computer simulation showed that 3D-Haar wavelets are better and closer to the exact solution but it is need to more time from 2D-Haar wavelets.

KEYWORDS

Haar Wavelets, Partial Differential Equations, Diffusion Equation, Poisson Equation

Share and Cite:

Nachaoui, A. , S. Al-Rawi, E. and F. Qasim, A. (2018) Solving Three Dimensional and Time Depending PDEs by Haar Wavelets Method. Open Access Library Journal, 5, 1-18. doi: 10.4236/oalib.1104496.

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