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Linearly implicit methods for the nonlinear Klein-Gordon equation
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DOI：10.1016/j.matcom.2024.12.019.png)
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Abstract
En 中文
We present energy-preserving linearly implicit integrators for the nonlinear Klein-Gordon equation, based on the polarization of the polynomial functions. They are symmetric, second- order accurate in time and space, and unconditionally stable. Instead of solving a nonlinear algebraic equation at every time step, the linearly implicit integrators only require solving a linear system, which reduces the computational cost. We propose three types of linearly implicit integrators for the nonlinear Klein-Gordon equation, that preserve the modified, polarized invariants, ensuring the stability of the solutions in long-time integration. Numerical results confirm the theoretical convergence orders and preservation of the Hamiltonians that guarantee the stability of the solutions in long-time simulation.
Keywords:
Hamiltonian systems
Linearly implicit integrator
Energy preservation
Stability
Journal
IF:
4.4
Papers:
786
Citations:
1.0W
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