A Numerical Method Based on Operator Splitting Collocation Scheme for Nonlinear Schrödinger Equation
In this paper, a second-order operator splitting method combined with the barycentric Lagrange interpolation collocation method is proposed for the nonlinear Schrödinger equation. The equation is split into linear and nonlinear parts: the linear part is solved by the barycentric Lagrange interpolati...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/29/1/6 |
| _version_ | 1797297521192599552 |
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| author | Mengli Yao Zhifeng Weng |
| author_facet | Mengli Yao Zhifeng Weng |
| author_sort | Mengli Yao |
| collection | DOAJ |
| description | In this paper, a second-order operator splitting method combined with the barycentric Lagrange interpolation collocation method is proposed for the nonlinear Schrödinger equation. The equation is split into linear and nonlinear parts: the linear part is solved by the barycentric Lagrange interpolation collocation method in space combined with the Crank–Nicolson scheme in time; the nonlinear part is solved analytically due to the availability of a closed-form solution, which avoids solving the nonlinear algebraic equation. Moreover, the consistency of the fully discretized scheme for the linear subproblem and error estimates of the operator splitting scheme are provided. The proposed numerical scheme is of spectral accuracy in space and of second-order accuracy in time, which greatly improves the computational efficiency. Numerical experiments are presented to confirm the accuracy, mass and energy conservation of the proposed method. |
| first_indexed | 2024-03-07T22:22:31Z |
| format | Article |
| id | doaj.art-1c5e0b3b0f0f4bb2b4f184511d4ed5e3 |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-07T22:22:31Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-1c5e0b3b0f0f4bb2b4f184511d4ed5e32024-02-23T15:26:20ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472024-01-01291610.3390/mca29010006A Numerical Method Based on Operator Splitting Collocation Scheme for Nonlinear Schrödinger EquationMengli Yao0Zhifeng Weng1Fujian Province University Key Laboratory of Computation Science, School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, ChinaFujian Province University Key Laboratory of Computation Science, School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, ChinaIn this paper, a second-order operator splitting method combined with the barycentric Lagrange interpolation collocation method is proposed for the nonlinear Schrödinger equation. The equation is split into linear and nonlinear parts: the linear part is solved by the barycentric Lagrange interpolation collocation method in space combined with the Crank–Nicolson scheme in time; the nonlinear part is solved analytically due to the availability of a closed-form solution, which avoids solving the nonlinear algebraic equation. Moreover, the consistency of the fully discretized scheme for the linear subproblem and error estimates of the operator splitting scheme are provided. The proposed numerical scheme is of spectral accuracy in space and of second-order accuracy in time, which greatly improves the computational efficiency. Numerical experiments are presented to confirm the accuracy, mass and energy conservation of the proposed method.https://www.mdpi.com/2297-8747/29/1/6nonlinear Schrödinger equationoperator splitting collocation methodbarycentric Lagrange interpolationconsistency analysisconvergence analysis |
| spellingShingle | Mengli Yao Zhifeng Weng A Numerical Method Based on Operator Splitting Collocation Scheme for Nonlinear Schrödinger Equation Mathematical and Computational Applications nonlinear Schrödinger equation operator splitting collocation method barycentric Lagrange interpolation consistency analysis convergence analysis |
| title | A Numerical Method Based on Operator Splitting Collocation Scheme for Nonlinear Schrödinger Equation |
| title_full | A Numerical Method Based on Operator Splitting Collocation Scheme for Nonlinear Schrödinger Equation |
| title_fullStr | A Numerical Method Based on Operator Splitting Collocation Scheme for Nonlinear Schrödinger Equation |
| title_full_unstemmed | A Numerical Method Based on Operator Splitting Collocation Scheme for Nonlinear Schrödinger Equation |
| title_short | A Numerical Method Based on Operator Splitting Collocation Scheme for Nonlinear Schrödinger Equation |
| title_sort | numerical method based on operator splitting collocation scheme for nonlinear schrodinger equation |
| topic | nonlinear Schrödinger equation operator splitting collocation method barycentric Lagrange interpolation consistency analysis convergence analysis |
| url | https://www.mdpi.com/2297-8747/29/1/6 |
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