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Special Issues Volume 2, Issue 3, August 2017, Page: 88-94
Haar Wavelet Solution of Poisson’s Equation and Their Block Structures
I. K. Youssef, Department of Mathematics, Ain Shams University, Cairo, Egypt
M. H. El Dewaik, Department of Basic Science, The British University, Cairo, Egypt
Received: Mar. 1, 2017;       Accepted: Mar. 13, 2017;       Published: Mar. 29, 2017
Abstract
The structure of the algebraic system which results from the use of Haar wavelet when solving Poisson’s equation is studied. Haar wavelet technique is used to solve Poisson’s equation on a unit square domain. The form of collocation points are used at the mid points of the subintervals i.e at the odd multiple of the sub interval length labeling. It is proved that the coefficient matrix has symmetric block structure. Comparison with the tridagonal block structure obtained by the finite difference with the natural ordering is introduced. The numerical results have illustrated the superiority of the use of Haar wavelet technique. The matrices obtained can be used for any equations containing the Laplace operator.
Keywords
Poisson’s Equation, Finite Difference, Wavelet, Haar Wavelet
I. K. Youssef, M. H. El Dewaik, Haar Wavelet Solution of Poisson’s Equation and Their Block Structures, American Journal of Mathematical and Computer Modelling. Vol. 2, No. 3, 2017, pp. 88-94. doi: 10.11648/j.ajmcm.20170203.13
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