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An exponentially convergent functional-discrete method for solving Sturm-Liouville problems with a potential including the Dirac \(\delta\)-function. (English) Zbl 1302.65172
Summary: We present a functional-discrete method for solving Sturm-Liouville problems with a potential that includes a function from \(L_1(0, 1)\) and the Dirac \(\delta\)-function. For both the linear and the nonlinear case sufficient conditions for an exponential rate of convergence of the method are obtained. The question of a possible software implementation of the method is discussed in detail. The theoretical results are successfully confirmed by a numerical example.
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
65Y15 Packaged methods for numerical algorithms
34L16 Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
Full Text: DOI
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