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High Order Scheme for Schrödinger Equation with Discontinuous Potential I: Immersed Interface Method

Published online by Cambridge University Press:  28 May 2015

Hao Wu
Hao Wu*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing, 10084, China
*
*Corresponding author.Email address:hwu@tsinghua.edu.cn
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Abstract

The immersed interface method is modified to compute Schrödinger equation with discontinuous potential. By building the jump conditions of the solution into the finite difference approximation near the interface, this method can give at least second order convergence rate for the numerical solution on uniform cartesian grids. The accuracy of this algorithm is tested via several numerical examples.

Keywords

35R0565M0681Q05Schrödinger equationdiscontinuous potentialimmersed interface methodfinite difference method

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Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 4 , November 2011, pp. 576 - 597
Copyright
Copyright © Global Science Press Limited 2011

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