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TT-M Finite Element Algorithm for the Coupled Schrödinger–Boussinesq Equations
- Source :
- Axioms, Vol 11, Iss 7, p 314 (2022)
- Publication Year :
- 2022
- Publisher :
- MDPI AG, 2022.
-
Abstract
- In this article, the coupled Schrödinger–Boussinesq equations are solved numerically using the finite element method combined with the time two-mesh (TT-M) fast algorithm. The spatial direction is discretized by the standard Galerkin finite element method, the temporal direction is approximated by the TT-M Crank–Nicolson scheme, and then the numerical scheme of TT-M finite element (FE) system is formulated. The method includes three main steps: for the first step, the nonlinear system is solved on the coarse time mesh; for the second step, by an interpolation formula, the numerical solutions at the fine time mesh point are computed based on the numerical solutions on the coarse mesh system; for the last step, the linearized temporal fine mesh system is constructed based on Taylor’s formula for two variables, and then the TT-M FE solutions can be obtained. Furthermore, theory analyses on the TT-M system including the stability and error estimations are conducted. Finally, a large number of numerical examples are provided to verify the accuracy of the algorithm, the correctness of theoretical results, and the computational efficiency with a comparison to the numerical results calculated by using the standard FE method.
Details
- Language :
- English
- ISSN :
- 20751680
- Volume :
- 11
- Issue :
- 7
- Database :
- Directory of Open Access Journals
- Journal :
- Axioms
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.fb263a2cc93f411cb518c549bfcfeca2
- Document Type :
- article
- Full Text :
- https://doi.org/10.3390/axioms11070314