Analytic approximation of transmutation operators and applications to highly accurate solution of spectral problems
arXiv:1306.2914 · doi:10.1016/j.cam.2014.07.022
Abstract
A method for approximate solution of spectral problems for Sturm-Liouville equations based on the construction of the Delsarte transmutation operators is presented. In fact the problem of numerical approximation of solutions and eigenvalues is reduced to approximation of a primitive of the potential by a finite linear combination of generalized wave polynomials introduced in arXiv:1208.5984, arXiv:1208.6166. The method allows one to compute both lower and higher eigendata with an extreme accuracy.
32 pages, 9 figures, 4 tables; Sections 6 and 7 extended, runtimes added
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- Construction of transmutation operators and hyperbolic pseudoanalytic functions
- A Neumann series of Bessel functions representation for solutions of perturbed Bessel equations
- Spectrum completion and inverse Sturm-Liouville problems
- Liouville transformation, analytic approximation of transmutation operators and solution of spectral problems
- Modified spectral parameter power series representations for solutions of Sturm-Liouville equations and their applications
- Reconstruction techniques for quantum trees
- Recovery of a potential on a quantum star graph from Weyl's matrix
- Method for solving inverse spectral problems on quantum star graphs
- Analytic approximation of transmutation operators and related systems of functions
- Modulated electromagnetic fields in inhomogeneous media, hyperbolic pseudoanalytic functions and transmutations
- Supersymmetric generalized power functions
- On Sturm-Liouville Equations with Several Spectral Parameters
- Analysis of the spectral symbol function for spectral approximation of a differential operator