论文标题
对数klein-gordon方程的两种正则提供能量的有限差异方法
Two regularized energy-preserving finite difference methods for the logarithmic Klein-Gordon equation
论文作者
论文摘要
我们提出并分析了两种正则有限差异方法，它们保留对数Klein-Gordon方程（Logkge）的能量。为了避免由Logkge的对数非线性引起的奇异性，我们提出了一个正规化的对数Klein-Gordon方程（Rlogkge），其较小的法规参数$ 0 <\ VAREPSILON \ ll1 $，以近似logkge，以与convergence Order $ o（\ varepsilon）$近似logkge。通过采用能量方法，逆不平等和非线性的截止技术来绑定数值解决方案，错误的错误（H^{2}+frac {τ^{2}} {\ varepsilon^{2}} $ \ varepsilon $。据报道，数值结果支持我们的结论。
We present and analyze two regularized finite difference methods which preserve energy of the logarithmic Klein-Gordon equation (LogKGE). In order to avoid singularity caused by the logarithmic nonlinearity of the LogKGE, we propose a regularized logarithmic Klein-Gordon equation (RLogKGE) with a small regulation parameter $0<\varepsilon\ll1$ to approximate the LogKGE with the convergence order $O(\varepsilon)$. By adopting the energy method, the inverse inequality, and the cut-off technique of the nonlinearity to bound the numerical solution, the error bound $O(h^{2}+\frac{τ^{2}}{\varepsilon^{2}})$ of the two schemes with the mesh size $h$, the time step $τ$ and the parameter $\varepsilon$. Numerical results are reported to support our conclusions.
