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   -> Volume 6, Issue 5


Preprint: Spline Wavelet ADI for 2-D Reaction-Diffusion Equations
 
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Wei Cai (wcai@uncc.edu)
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PostPosted: Tue May 06, 1997 10:12 pm    
Subject: Preprint: Spline Wavelet ADI for 2-D Reaction-Diffusion Equations
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#9 Preprint: Spline Wavelet ADI for 2-D Reaction-Diffusion Equations

An Adaptive Spline Wavelet ADI (SW-ADI) Method
for
Two-Dimensional Reaction-Diffusion Equations

Wei Cai and Wu Zhang

Department of Mathematics
University of North Carolina at Charlotte
Charlotte, NC 28223

Abstract

We study a Spline Wavelet Alternative Direction Implicit (SW-ADI)
algorithm for solving two-dimensional reaction diffusion
equations. This algorithm is based on a collocation method for PDEs
with a specially designed spline wavelet for the Sobolev space on a
closed interval I. By using the tensor product nature of adaptive
wavelet meshes, we propose a SW-ADI method for two-dimensional
problems. The proposed SW-ADI method is an efficient time dependent
adaptive method with second order accuracy for solutions with
localized phenomena, such as in flame propagations. Issues like new
boundary wavelets for more accurate boundary conditions, adaptive
strategy for two-dimensional meshes, data structure and storage and
implementation details, and numerical results will be discussed.

Instruction to get the paper:

The compressed ps files for the paper and figures can be accessed by
anonymous ftp to ftp.uncc.edu in the directory cas/math/wcai. Please
uncompress all files before printing.
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