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arXiv · 1907.02122

Linearly implicit local and global energy-preserving methods for PDEs with a cubic Hamiltonian

Sølve Eidnes·Lu Li
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Abstract

We present linearly implicit methods that preserve discrete approximations to local and global energy conservation laws for multi-symplectic PDEs with cubic invariants. The methods are tested on the one-dimensional Korteweg-de Vries equation and the two-dimensional Zakharov-Kuznetsov equation; the numerical simulations confirm the conservative properties of the methods, and demonstrate their good stability properties and superior running speed when compared to fully implicit schemes.

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Sølve Eidnes, Lu Li. 2020-07-12. Linearly implicit local and global energy-preserving methods for PDEs with a cubic Hamiltonian. https://arxiv.org/abs/1907.02122

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