Error estimate and long-time energy conservation of a symmetric low-regularity integrator for nonlinear Klein-Gordon equation
CoRR(2023)
摘要
In this paper, we formulate and analyse a symmetric low-regularity integrator
for solving the nonlinear Klein-Gordon equation in the $d$-dimensional space
with $d=1,2,3$. The integrator is constructed based on the two-step
trigonometric method and the proposed integrator has a simple form. Error
estimates are rigorously presented to show that the integrator can achieve
second-order time accuracy in the energy space under the regularity requirement
in $H^{1+\frac{d}{4}}\times H^{\frac{d}{4}}$. Moreover, the time symmetry of
the scheme ensures the good long-time energy conservation which is rigorously
proved by the technique of modulated Fourier expansions. A numerical test is
presented and the numerical results demonstrate the superiorities of the new
integrator over some existing methods.
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