Exponentially convergent functional-discrete method for eigenvalue   transmission problems with discontinuous flux and potential as a function in   the space $L_1$
  Based on the functional-discrete technique (FD-method), an algorithm for eigenvalue transmission problems with discontinuous flux and integrable potential is developed. The case of the potential as a function belonging to the functional space $L_1$ is studied for both linear and nonlinear eigenvalue problems. The sufficient conditions providing superexponential convergence rate of the method were obtained. Numerical examples are presented to support the theory. Based on the numerical examples and the convergence results, conclusion about analytical properties of eigensolutions for nonself-adjoint differential operators is made. 
Volodymyr Makarov, Nataliya Rossokhata and Denis Dragunov
math.NA