Computing eigenpairs of two-parameter Sturm-Liouville systems using the bivariate sinc-Gauss formula

The use of sampling methods in computing eigenpairs of twoparameter boundary value problems is extremely rare. As far as we know, there are only two studies up to now using the bivariate version of the classical and regularized sampling series. These series have a slow convergence rate. In this paper, we use the bivariate sinc-Gauss sampling formula that was proposed in [6] to construct a new sampling method to compute eigenpairs of a two-parameter Sturm-Liouville system. The convergence rate of this method will be of exponential order, i.e. O(e^-δN/√N) where δ is a positive number and N is the number of terms in the bivariate sinc-Gaussian formula. We estimate the amplitude error associated to this formula, which gives us the possibility to establish the rigorous error analysis of this method. Numerical illustrative examples are presented to demonstrate our method in comparison with the results of the bivariate classical sampling method.