Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs

Abstract Two classes of efficient and robust schemes are proposed for the general multi-symplectic Hamiltonian systems using the invariant energy quadratization (IEQ) approach. The schemes are linear, second-order accurate, local energy-preserving, and preserve the global energy. They are not restricted to specific forms of the nonlinear part of the state function, and only require solving linear equations at each time step. We applied the new schemes to various multi-symplectic Hamiltonian PDEs to demonstrate their effectiveness, computational efficiency and accuracy.

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