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On the stability of the FDTD method for solving a time‐dependent Schrödinger equation
Author(s) -
Dai Weizhong,
Li Guang,
Nassar Raja,
Su Shengjun
Publication year - 2005
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20082
Subject(s) - finite difference time domain method , mathematics , stability (learning theory) , scheme (mathematics) , partial differential equation , time domain , mathematical analysis , schrödinger equation , computer science , physics , quantum mechanics , machine learning , computer vision
The finite difference time domain (FDTD) method is often employed in simulation of electromagnetic fields. The scheme is explicit and two‐level in time. However, it is not clear what the time step, Δt, should be when the FDTD method is applied for solving a time‐dependent Schrödinger equation. In this study, we analyze the stability of the FDTD scheme for solving the time‐dependent Schrödinger equation. A condition for choosing the time step is obtained in order that the scheme is stable. A numerical example is illustrated. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005