Wavelet Method for Numerical Solution of Parabolic Equations. (27th February 2014)

• Record Type: Journal Article
• Authors: Choudhury, A. H.
• Other Names: Zhao Fu-Yun Academic Editor.
• Is Part Of: Journal of computational engineering. Volume 2014(2014)
• Publication Date: 2014-02-27
• Subjects: Engineering mathematics -- Periodicals; Engineering -- Mathematical models -- Periodicals; Engineering -- Mathematical models; Engineering mathematics; Periodicals; 620.00285
• DOI: 10.1155/2014/346731
• Languages: English
• ISSNs: 2356-7260

Abstract

Abstract : We derive a highly accurate numerical method for the solution of parabolic partial differential equations in one space dimension using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method using some special types of basis functions obtained by integrating Daubechies functions which are compactly supported and differentiable. The time variable is discretized by using various classical finite difference schemes. Theoretical and numerical results are obtained for problems of diffusion, diffusion-reaction, convection-diffusion, and convection-diffusion-reaction with Dirichlet, mixed, and Neumann boundary conditions. The computed solutions are highly favourable as compared to the exact solutions.