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 (lavoro effettuato nell'ambito di ricerche finanziate dall'INdAM).
Solving the time-fractional Schrödinger equation by Krylov projections methods
GARRAPPA, Roberto;
2015-01-01
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 (lavoro effettuato nell'ambito di ricerche finanziate dall'INdAM).File in questo prodotto:
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