Solving Singularly Perturbed Reaction Diffusion Problems Using Wavelet Optimized Finite Difference and Cubic Spline Adaptive Wavelet Scheme
Year: 2008
Author: Vivek Kumar
International Journal of Numerical Analysis and Modeling, Vol. 5 (2008), Iss. 2 : pp. 270–285
Abstract
In this paper singularly perturbed reaction diffusion equations of elliptic and parabolic types have been discussed using wavelet optimized finite difference (WOFD) method based on an interpolating wavelet transform using cubic spline on dyadic points as discussed in [1]. Adaptive feature is performed automatically by thresholding the wavelet coefficients. WOFD [2] works by using adaptive wavelet to generate an irregular grid which is then exploited for the finite difference method. Numerical examples are presented for elliptic and parabolic problems and comparisons have been made using cubic spline and WOFD. The proposed adaptive method is very effective for studying singular perturbation problems in term of adaptive grid generation and CPU time.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-IJNAM-811
International Journal of Numerical Analysis and Modeling, Vol. 5 (2008), Iss. 2 : pp. 270–285
Published online: 2008-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: singularly perturbed reaction diffusion problems WOFD splines wavelets multiresolution analysis fast discrete wavelet transform Lagrangian finite difference.