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• W4283710814 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." @default.
• W4283710814 created "2022-06-30" @default.
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• W4283710814 date "2022-06-28" @default.
• W4283710814 modified "2023-10-14" @default.
• W4283710814 title "TT-M Finite Element Algorithm for the Coupled Schrödinger–Boussinesq Equations" @default.
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• W4283710814 doi "https://doi.org/10.3390/axioms11070314" @default.
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