INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND - Volume 6, Issue 8,, December 2017 (Special Issue)

Pages: 20-26

Date of Publication: 24-Dec-2017

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Multigrid Method for the Numerical Solution of Parabolic Partial Differential Equations using Biorthogonal Wavelets

Author: S. C. Shiralashetti?a L. M. Angadi??b S. I. Hanaji???c L. B. Lamani????

Category: Engineering, Science and Mathematics

Abstract:

In this paper, we proposed multi-grid method for the numerical solution of parabolic partial differential equations (PDEs) using biorthogonal wavelets. The standard multigrid procedure performs poorly or may break down when used to solve certain PDEs with discontinuous or highly oscillatory coefficients and also involve some difficulty to observe fast convergence in low computational time. To overcome this, we used Biorthogonal Wavelet Based Multigrid Method for solving parabolic PDEs in which the system of equations arising from the finite difference discretization is represented in wavelet bases. Some of the test problems are presented to demonstrate the validity and applicability of the proposed method.

Keywords: Wavelet multigrid; Biorthogonal wavelets; Filter coefficients; Parabolic PDEs.