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• W2999692471 abstract "This article is concerned with the numerical solution to the time-dependent Schrödinger equation on an infinite domain. Two exact artificial boundary conditions are introduced to reduce the original problem into an initial boundary value problem with a finite computational domain. The artificial boundary conditions involve the 1/2 order fractional derivative in t. Then, a fully discrete explicit three-level difference scheme is derived. The truncation errors are analyzed in detail. The stability and convergence with the convergence order of O(h3/2 + τh−1/2) are proved under the condition τ/h2 < 1/2 by the energy method. A numerical example is given to demonstrate the accuracy and efficiency of the proposed method. Two open problems are brought forward at the end of the article." @default.
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• W2999692471 date "2006-12-01" @default.
• W2999692471 modified "2023-09-27" @default.
• W2999692471 title "The stability and convergence of an explicit difference scheme for the Schrödinger equation on an infinite domain by using artificial boundary conditions" @default.
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• W2999692471 doi "https://doi.org/10.1016/j.jcp.2006.07.001" @default.
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