Based on the functional-discrete technique (FD-method), an algorithm for solving eigenvalue transmission problems with a discontinuous flux and the 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.
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