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

12 Jul 2020  ·  Eidnes Sølve, Li Lu ·

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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Numerical Analysis Numerical Analysis