During the past few years, a new algorithmic paradigm for adaptive wavelet schemes was developed. First approaches covered elliptic problems, but meanwhile, the class of feasible problems could be significantly enlarged, including even certain nonlinear problems. This thesis will present and analyze routines for key tasks arising in connection with those schemes. The central point will be a so called recovery scheme that allows to compute arrays of wavelet coefficients efficiently by treating the array as a whole instead of treating each entry separately by quadrature schemes. The tools and methods we develop are realized in a C++ implementation by the author, which we present in form of a schematic overview. All numerical studies presented in the thesis are based on this implementation
