Quasi-trefftz spectral method for separable linear elliptic equations

A new numerical method QTSM which was earlier suggested for solving boundary value problems with elliptic operators with constant coefficients is applied to separable, second-order elliptic equations with varying coefficients. The problems in irregular domains are considered. The method combines the properties of the boundary methods with the spectral representation of the solution in the form of expansion over the eigenfunctions of some Sturm-Liouville problem. The method is tested on several one- and two-dimensional problems with exact analytic solution. The possibilities of further developments of the method are discussed.