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Based on the functional-discrete technique (FD-method), an algorithm foreigenvalue transmission problems with discontinuous flux and integrablepotential is developed. The case of the potential as a function belonging tothe functional space $L_1$ is studied for both linear and nonlinear eigenvalueproblems. The sufficient conditions providing superexponential convergence rateof the method were obtained. Numerical examples are presented to support thetheory. Based on the numerical examples and the convergence results, conclusionabout analytical properties of eigensolutions for nonself-adjoint differentialoperators is made.

Exponentially convergent functional-discrete method for eigenvalue  transmission problems with discontinuous flux and potential as a function in  the space $L_1$