Numerical Method for Stochastic Nonlinear Schrödinger Equation Driven by Multivariate Gaussian Measure: Algorithms and Applications
In this paper, we present a novel Galerkin spectral method for numerically solving the stochastic nonlinear Schrödinger (NLS) equation driven by multivariate Gaussian random variables, including the nonlinear term. Our approach involves deriving the tensor product of triple random orthogonal basis a...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2023-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/8007384 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832546587355643904 |
|---|---|
| author | Hongling Xie |
| author_facet | Hongling Xie |
| author_sort | Hongling Xie |
| collection | DOAJ |
| description | In this paper, we present a novel Galerkin spectral method for numerically solving the stochastic nonlinear Schrödinger (NLS) equation driven by multivariate Gaussian random variables, including the nonlinear term. Our approach involves deriving the tensor product of triple random orthogonal basis and random functions, which enables us to effectively handle the stochasticity and nonlinear term in the equation. We apply this newly proposed method to solve both one- and two-dimensional stochastic NLS equations, providing detailed analysis and comparing the results with Monte Carlo simulation. In addition, the proposed method is applied to the stochastic Ginzburg–Landau equation. Our method exhibits excellent performance in both spatial and random spaces, achieving spectral accuracy in the numerical solutions. |
| format | Article |
| id | doaj-art-2cb63537adda4311807d4332a125bd6f |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-2cb63537adda4311807d4332a125bd6f2025-02-03T06:47:41ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/8007384Numerical Method for Stochastic Nonlinear Schrödinger Equation Driven by Multivariate Gaussian Measure: Algorithms and ApplicationsHongling Xie0School of Mathematics and StatisticsIn this paper, we present a novel Galerkin spectral method for numerically solving the stochastic nonlinear Schrödinger (NLS) equation driven by multivariate Gaussian random variables, including the nonlinear term. Our approach involves deriving the tensor product of triple random orthogonal basis and random functions, which enables us to effectively handle the stochasticity and nonlinear term in the equation. We apply this newly proposed method to solve both one- and two-dimensional stochastic NLS equations, providing detailed analysis and comparing the results with Monte Carlo simulation. In addition, the proposed method is applied to the stochastic Ginzburg–Landau equation. Our method exhibits excellent performance in both spatial and random spaces, achieving spectral accuracy in the numerical solutions.http://dx.doi.org/10.1155/2023/8007384 |
| spellingShingle | Hongling Xie Numerical Method for Stochastic Nonlinear Schrödinger Equation Driven by Multivariate Gaussian Measure: Algorithms and Applications Journal of Mathematics |
| title | Numerical Method for Stochastic Nonlinear Schrödinger Equation Driven by Multivariate Gaussian Measure: Algorithms and Applications |
| title_full | Numerical Method for Stochastic Nonlinear Schrödinger Equation Driven by Multivariate Gaussian Measure: Algorithms and Applications |
| title_fullStr | Numerical Method for Stochastic Nonlinear Schrödinger Equation Driven by Multivariate Gaussian Measure: Algorithms and Applications |
| title_full_unstemmed | Numerical Method for Stochastic Nonlinear Schrödinger Equation Driven by Multivariate Gaussian Measure: Algorithms and Applications |
| title_short | Numerical Method for Stochastic Nonlinear Schrödinger Equation Driven by Multivariate Gaussian Measure: Algorithms and Applications |
| title_sort | numerical method for stochastic nonlinear schrodinger equation driven by multivariate gaussian measure algorithms and applications |
| url | http://dx.doi.org/10.1155/2023/8007384 |
| work_keys_str_mv | AT honglingxie numericalmethodforstochasticnonlinearschrodingerequationdrivenbymultivariategaussianmeasurealgorithmsandapplications |