Solving Singularly Perturbed Reaction Diffusion Problems Using Wavelet Optimized Finite Difference and Cubic Spline Adaptive Wavelet Scheme

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.

Author Details

Vivek Kumar