Wavelet or multiresolution analysis (MRA) is widely applied in advanced data compression algorithms, solving differential equations, and some approaches have already applied this technique in describing electromagnetic fields. The main advantage of the application of MRA is its adaptivity and flexibility. Since the details of the electromagnetic field are not distributed equally over different parts of the system (i.e., the description of some parts need finer details, while others are easily represented at low resolution level), locally different resolution levels can be applied. Wavelet based adaptive solution possibilities of differential equations of electromagnetic field are investigated in the followings. The adaptivity of the method means in this case, that the refinement level of the solution can be increased locally, if the accuracy needs it, during the calculations. The applicability of the eigenvalue-type differential equation solving method is illustrated by solution of microwave wave-equations of cavity resonators.