Abstract
A procedure is proposed to construct solutions of the double confluent Heun equation with a determinate behaviour at the singular points. The connection factors are expressed as quotients of Wronskians of the involved solutions. Asymptotic expansions are used in the computation of those Wronskians. The feasibility of the method is shown in an example, namely, the Schrödinger equation with a quasi-exactly-solvable potential.
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In memoriam Prof. Luigi Gatteschi.
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Abad, J., Gómez, F.J. & Sesma, J. An algorithm to obtain global solutions of the double confluent Heun equation. Numer Algor 49, 33–51 (2008). https://doi.org/10.1007/s11075-008-9197-4
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DOI: https://doi.org/10.1007/s11075-008-9197-4
Keywords
- Differential equations
- Double confluent Heun equation
- Connection problem
- Stokes phenomenon
- Multiplicative solutions
- Asymptotic solutions
- Schrödinger equation
- Quasi-exactly-solvable potentials