Unconditional \(L_\infty\) convergence of a compact ADI scheme for coupled nonlinear Schrödinger system (Q1986171)
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scientific article; zbMATH DE number 7188155
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Unconditional \(L_\infty\) convergence of a compact ADI scheme for coupled nonlinear Schrödinger system |
scientific article; zbMATH DE number 7188155 |
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Unconditional \(L_\infty\) convergence of a compact ADI scheme for coupled nonlinear Schrödinger system (English)
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7 April 2020
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A three-level compact ADI scheme is developed to solve the two-dimensional coupled nonlinear Schrödinger (CNLS) system for which, using \(L_{\infty}\) estimates, it is proved that the new scheme is second-order accurate in time variable and fourth-order accurate in space variable, and stable. Numerical experiments demonstrate that the method is highly accurate and efficient. It can be directly extended to the three-dimensional CNLS system and multi-dimensional nonlinear Schödinger-type equations.
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compact ADI scheme
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coupled nonlinear Schrödinger system
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convergence in \(L_\infty\) norm
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