Cubic spline Adaptive Wavelet Scheme to Solve singularly perturbed Reaction Diffusion Problems

In this paper, the collocation method proposed by Cai and Wang1 has been reviewed in detail to solve singularly perturbed reaction diffusion equation of elliptic and parabolic types. The method is based on an interpolating wavelet transform using cubic spline on dyadic points. Adaptive feature is performed automatically by thresholding the wavelet coefficients. Numerical examples are presented for elliptic and parabolic problems. The purposed method comes up as a powerful tool for studying singular perturbation problems in term of effective grid generation and CPU time.