Computing of eigenvalues of sturm-liouville problems with eigenparameter dependent boundary conditions

The purpose of this article is to use the classical sampling theorem, WKS sampling theorem, to derive approximate values of the eigenvalues of the Sturm-Liouville problems with eigenparameter in the boundary conditions. Error analysis is used to give estimates of the associated error. Higher order approximations are also drived, which lead to more complicated computations. We give some examples and make companions with existing results.