Application of wavelets to predict solid fuel combustion

The application of wavelets to the solution of partial differential equations arising in different areas of physics and engineering is a new field of research. In this work partial differential equations are discretised using wavelets as basis functions. Beside a short introduction to wavelets the wavelet collocation algorithm developed by Vasilyev et al. (1995) is described. The basic idea behind the multilevel approximation is that a function can be approximated as a linear combination of wavelets having different scales and locations. Adaption is achieved by retaining only those wavelets whose coefficients are greater than a given threshold. This property allows local grid refinement up to an arbitrary small scale without a drastic increase of collocation points. The capabilities of the method are demonstrated with several examples which show the advantages of the method in resolving locally steep gradients.