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Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 576-597. |
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High Order Scheme for Schrodinger Equation with Discontinuous Potential I: Immersed Interface Method Hao Wu 1* 1 Department of Mathematical Sciences, Tsinghua University, Beijing, 10084, China.Received 22 October 2010; Accepted (in revised version) 21 March 2011 Abstract The immersed interface method is modified to compute Schrodinger 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. AMS subject classifications: 35R05, 65M06, 81Q05Key words: Schrodinger equation, discontinuous potential, immersed interface method, finite difference method. *Corresponding author. Email: hwu@tsinghua.edu.cn (H. Wu) |