An efficient hybrid scheme for solving time-space fractional Schr\"{o}dinger equation with error analysis

Fatemeh Hashemi, Esmaeil Hesameddini, Ameneh Taleei

Abstract


A numerical approximation combining the fast finite difference method in time and the finite element method in space is studied to solve the distributed-order time and Riesz space fractional Schr\"{o}dinger equation. In this work, a fast evaluation of the distributed-order time fractional derivative based on graded time mesh is applied to the time approximation of this equation. Also, the finite element method is used for space approximation. Moreover, the stability and convergence of the resulting discrete scheme are discussed. Finally, some numerical examples are presented to confirm the theoretical results.


Keywords


Schr\"{o}dinger equation; distributed-order fractional equation; fast finite difference method; finite element method; error analysis

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