The time-fractional Schrödinger equation is a fundamental topic in physics and its numerical solution is still an open problem. Here we start from the possibility to express its solution by means of the Mittag–Leffler function; then we analyze some approaches based on the Krylov projection methods to approximate this function; their convergence properties are discussed, together with related issues. Numerical tests are presented to confirm the strength of the approach under investigation.
Solving the time-fractional Schrödinger equation by Krylov projections methods / R., Garrappa; Moret, Igor; M., Popolizio. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - ELETTRONICO. - (2014), pp. 1-20. [10.1016/j.jcp.2014.09.023]
Solving the time-fractional Schrödinger equation by Krylov projections methods
MORET, IGOR;
2014-01-01
Abstract
The time-fractional Schrödinger equation is a fundamental topic in physics and its numerical solution is still an open problem. Here we start from the possibility to express its solution by means of the Mittag–Leffler function; then we analyze some approaches based on the Krylov projection methods to approximate this function; their convergence properties are discussed, together with related issues. Numerical tests are presented to confirm the strength of the approach under investigation.Pubblicazioni consigliate
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