  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.
