Implementation and Testing an Algorithm for a Wavelet Collocation Method in Mathematica
Marco Schuchmann, M. Rasguljajew · 2013
Abstract — During a research project we described an algorithm for a wavelet collocation method. This algorithm can be applied on ODEs with various orders and even to PDEs. We have implemented the algorithm in a Mathematica module and applied several tests. The applied wavelet collocation method is costly, like collocation method are costly in general. But for stiff or unstable problems it has an advantage and for these cases explicit methods cannot be used. We used a few test problems and in some problems, the Mathematica function for numerical solving of ODEs (NDSolve) has problems, but not our Module. We used the Shannon wavelet in our module, but it can be modified for other wavelets. The ODE can be given in implicit form.