Symbolic algorithm of the functional-discrete method for a Sturm-Liouville problem with a polynomial potential

DOI10.1515/CMAM-2017-0040zbMath1412.65059arXiv1708.03567OpenAlexW3103255134MaRDI QIDQ2416921

Nataliia M. Romaniuk, Volodymyr L. Makarov

Publication date: 24 May 2019

Published in: Computational Methods in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.03567

zbMATH Keywords

eigenvalue problemSturm-Liouville problemsymbolic algorithmpolynomial potentialfunctional-discrete methodsuper-exponentially convergence rate

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Stability and convergence of numerical methods for ordinary differential equations (65L20) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators (34L16) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15) Boundary eigenvalue problems for ordinary differential equations (34B09)

Related Items (2)

Exponentially convergent symbolic algorithm of the functional-discrete method for the fourth order Sturm-Liouville problems with polynomial coefficients ⋮ A criterion of solvability of resonant equations and construction of their solutions

Uses Software

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• How many numerical eigenvalues can we trust?
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• Anwendung eines direkten Verfahrens zur numerischen Behandlung von selbstadjungierten, positiv definiten Eigenwertaufgaben bei linearen gewöhnlichen Differentialgleichungen mit stückweise stetigen Koeffizientenfunktionen
• The FD method for first-order linear hyperbolic differential equations with piecewise smooth coefficients
• Estimating the Eigenvalues of Sturm–Liouville Problems by Approximating the Differential Equation

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