论文标题
非局部正规化KDV型方程的半差异数值方案
A semi-discrete numerical scheme for nonlocally regularized KdV-type equations
论文作者
论文摘要
考虑了一类通用的KDV型波方程，并考虑了空间中卷积类型非局部性正规的。该类别与以前通过添加涉及三阶导数的线性卷积项所研究的非线性非局部单向波方程的类别不同。为了解决Cauchy问题，我们提出了一种基于统一的空间离散化的半差异数值方法，这是当前作者先前发表的工作的扩展。当网格大小为零时，我们证明了数值方法的均匀收敛。我们还证明，如果有限域足够大，则将定位到有限域产生的定位误差显着小于给定阈值。为了说明理论结果，对Rosenau-KDV方程，Rosenau-BBM-KDV方程和卷积型跨式差异方程进行了一些数值实验。对内核函数的三个特定选择进行的实验证实了我们提供的错误估计。
A general class of KdV-type wave equations regularized with a convolution-type nonlocality in space is considered. The class differs from the class of the nonlinear nonlocal unidirectional wave equations previously studied by the addition of a linear convolution term involving third-order derivative. To solve the Cauchy problem we propose a semi-discrete numerical method based on a uniform spatial discretization, that is an extension of a previously published work of the present authors. We prove uniform convergence of the numerical method as the mesh size goes to zero. We also prove that the localization error resulting from localization to a finite domain is significantly less than a given threshold if the finite domain is large enough. To illustrate the theoretical results, some numerical experiments are carried out for the Rosenau-KdV equation, the Rosenau-BBM-KdV equation and a convolution-type integro-differential equation. The experiments conducted for three particular choices of the kernel function confirm the error estimates that we provide.
