Solving Three Dimensional and Time Depending PDEs by Haar Wavelets Method
Résumé
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.