在Crank-Nicolson格式下解对流扩散问题的移动网格方法

Crank-Nicolson Difference Scheme for Convection-Diffusion Problem by Using Moving Mesh Method

对一类含源项非定常奇异摄动对流扩散问题,作者构造了移动网格下的Crank-Nicolson差分格式,介绍了移动网格的网格迭代方法和算法,并通过数值实验实现了算法,将求解的误差与均匀网格下求解的误差相比较,证明了在移动网格下运用Crank-Nicolson差分格式求解这类奇异摄动问题能有效的克服数值振荡,得到较好的结果.

The authors construct Crank-Nicolson difference scheme on moving mesh for a class of non-constant singularly perturbed convection-diffusion problem with source term,and introduce the iterative method and algorithm of moving mesh.The authors compare the error on moving mesh and uniform mesh by numerical experiments,and prove that it can decrease numerical oscillation effectively when using Crank-Nicolson difference scheme on moving mesh.