Wavelet optimized finite difference method with non-static re-gridding

The main aim of wavelet-based numerical methods for solving partial differential equations is to develop adaptive schemes, in order to achieve accuracy and computational efficiency. The wavelet optimized finite difference method (WOFD) uses wavelets to generate appropriate grids to apply finite difference method. Its standard implementation carries out static-re-griddings after a fixed number of time steps. We present an effective implementation of WOFD method that reduces the number of static-re-griddings hence leading to reduction of FLOPS, without significant loss of accuracy. Numerical experiments are performed on different cases of heat and Schrödinger equations.