Algebraically stable high-order multi-physical property-preserving methods for the regularized long-wave equation. (English) Zbl 07885880
Summary: In this paper, based on the framework of the supplementary variable method, we present two classes of high-order, linearized, structure-preserving algorithms for simulating the regularized long-wave equation. The suggested schemes are as accurate and efficient as the recently proposed schemes in Jiang et al. (2022) [20], but share the nice features in two folds: (i) the first type of schemes conserves the original energy conservation, as opposed to a modified quadratic energy in [20]; (ii) the second type of schemes fills the gap of [20] by constructing high-order linear algorithms that preserve both two invariants of mass and momentum. We discretize the SVM systems by employing the algebraically stable Runge-Kutta method together with the prediction-correction technique in time and the Fourier pseudo-spectral method in space. The implementation benefits from solving the optimization problems subject to PDE constraints. Numerical examples and some comparisons are provided to show the effectiveness, accuracy and performance of the proposed schemes.
MSC:
| 65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 35Qxx | Partial differential equations of mathematical physics and other areas of application |
| 65Lxx | Numerical methods for ordinary differential equations |
Keywords:
regularized long-wave equation; supplementary variable method; optimization problem; algebraically stable RK method; prediction-correction; Fourier pseudo-spectral methodReferences:
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