论文标题
使用曲柄 - 尼古尔森方案用于抛物线PDE的曲柄 - 尼古尔森方案时，Quang分裂的超对conververcectect
Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions
论文作者
论文摘要
我们表明，当使用曲柄 - 尼科尔森方法求解扩散方程时，使用不均匀的一般斜边界条件应用于扩散反应方程的strang分裂方法是二的，而如果通常使用其他runge-kutta方案，甚至在扩散部分中使用其他精确流动本身。当源术语仅取决于空间变量时，我们证明了这些结果，这一假设使得分裂方案等效于曲柄 - 尼科尔森方法本身应用于整个问题。数值实验表明，二阶收敛持续使用一般的非线性。
We show that the Strang splitting method applied to a diffusion-reaction equation with inhomogeneous general oblique boundary conditions is of order two when the diffusion equation is solved with the Crank-Nicolson method, while order reduction occurs in general if using other Runge-Kutta schemes or even the exact flow itself for the diffusion part. We prove these results when the source term only depends on the space variable, an assumption which makes the splitting scheme equivalent to the Crank-Nicolson method itself applied to the whole problem. Numerical experiments suggest that the second order convergence persists with general nonlinearities.
