Numerical Strategies for Solving Multiparameter Spectral Problems

We focus on the solution of multiparameter spectral problems, and in particular on some strategies to compute coarse approximations of selected eigenparameters depending on the number of oscillations of the associated eigenfunctions. Since the computation of the eigenparameters is crucial in codes for multiparameter problems based on finite differences, we herein present two strategies. The first one is an iterative algorithm computing solutions as limit of a set of decoupled problems (much easier to solve). The second one solves problems depending on a parameter sigma is an element of [0, 1], that give back the original problem only when sigma = 1. We compare the strategies by using well known test problems with two and three parameters.