Wavelet optimized finite difference method using interpolating wavelets for solving singularly perturbed problems

Awavelet optimized finite difference (WOFD) method is presented for adaptively solving a class of singularly perturbed elliptic and parabolic problems. The method is based on an interpolating wavelet transform using polynomial interpolation on dyadic grids. Adaptive feature is performed automatically by thresholding the wavelet coefficients. Numerical examples for elliptic and parabolic problems are provided. The proposed method proves to be a better alternative for dealing singular perturbation problems in terms of automatic grid generation and CPU time.