论文标题
对数klein-gordon方程的正则有限差异方法
Regularized finite difference methods for the logarithmic Klein-Gordon equation
论文作者
论文摘要
我们建议并分析对数Klein-Gordon方程（Logkge）的两种正则有限差异方法。由于logkge的对数非线性引起的爆炸现象，很难构建数值方案并建立其误差界限。为了避免奇异性，我们提出一个带有小的正规参数$ 0 <\ varepsilon \ ll1 $的正规化对数klein-gordon方程（RLOGKGE）。此外，采用了两种有限差异方法来解决正常的对数klein-gordon方程（RLOGKGE），并根据网格尺寸$ h $，时间步长$τ$和小型正则化参数$ \ varepsilon $估算了严格的错误界限。最后，进行数值实验以验证我们对两种数值方法的错误估计，并使用线性收敛顺序$ O（\ varepsilon）$从logkge到rlogkge产生收敛。
We propose and analyze two regularized finite difference methods for the logarithmic Klein-Gordon equation (LogKGE). Due to the blowup phenomena caused by the logarithmic nonlinearity of the LogKGE, it is difficult to construct numerical schemes and establish their error bounds. In order to avoid singularity, we present a regularized logarithmic Klein-Gordon equation (RLogKGE) with a small regularized parameter $0<\varepsilon\ll1$. Besides, two finite difference methods are adopted to solve the regularized logarithmic Klein-Gordon equation (RLogKGE) and rigorous error bounds are estimated in terms of the mesh size $h$, time step $τ$, and the small regularized parameter $\varepsilon$. Finally, numerical experiments are carried out to verify our error estimates of the two numerical methods and the convergence results from the LogKGE to the RLogKGE with the linear convergence order $O(\varepsilon)$.
