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Beylkin, G. and Keiser, J.M. (1977) An Adaptive Pseudo-Wavelet Approach for Solving Nonlinear Partial Differential Equations. In: Dahmen, W., Kurdila, A.J. and Oswald, P., Eds., Multi-Scale Wavelet Methods for Partial Differential Equations, Academic Press, San Diego, 137-197.

has been cited by the following article:

• TITLE: Solving Three Dimensional and Time Depending PDEs by Haar Wavelets Method

  AUTHORS: Abdeljalil Nachaoui, Ekhlass S. Al-Rawi, Ahmed F. Qasim

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

  JOURNAL NAME: Open Access Library Journal, Vol.5 No.5, May 24, 2018

  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.