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Volume 4, Issue 4
High Order Scheme for Schrödinger Equation with Discontinuous Potential I: Immersed Interface Method

Hao Wu

DOI: 10.4208/nmtma.2011.m1036

Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 576-597.

Published online: 2011-04

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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

Schrödinger equation, discontinuous potential, immersed interface method, finite difference method.

  • AMS Subject Headings

35R05, 65M06, 81Q05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-4-576, author = {Wu , Hao}, title = {High Order Scheme for Schrödinger Equation with Discontinuous Potential I: Immersed Interface Method}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2011}, volume = {4}, number = {4}, pages = {576--597}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2011.m1036}, url = {http://global-sci.org/intro/article_detail/nmtma/5984.html} }
TY - JOUR T1 - High Order Scheme for Schrödinger Equation with Discontinuous Potential I: Immersed Interface Method AU - Wu , Hao JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 576 EP - 597 PY - 2011 DA - 2011/04 SN - 4 DO - http://doi.org/10.4208/nmtma.2011.m1036 UR - https://global-sci.org/intro/article_detail/nmtma/5984.html KW - Schrödinger equation, discontinuous potential, immersed interface method, finite difference method. AB -

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.

Wu , Hao. (2011). High Order Scheme for Schrödinger Equation with Discontinuous Potential I: Immersed Interface Method. Numerical Mathematics: Theory, Methods and Applications. 4 (4). 576-597. doi:10.4208/nmtma.2011.m1036
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