An Adaptive Spline Wavelet ADI (SW-ADI) Method for Two-Dimensional Reaction–Diffusion Equations
✍ Scribed by Wei Cai; Wu Zhang
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 404 KB
- Volume
- 139
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
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 H 2 (I ) 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.