• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>International journal of computer mathematics >Crank-Nicolson finite difference method based on a midpoint upwind scheme on a non-uniform mesh for time-dependent singularly perturbed convection-diffusion equations
【24h】

Crank-Nicolson finite difference method based on a midpoint upwind scheme on a non-uniform mesh for time-dependent singularly perturbed convection-diffusion equations

机译：基于时空奇异摄动对流扩散方程的非均匀网格上基于中点迎风格式的Crank-Nicolson有限差分方法

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

A numerical approach is proposed to examine the singularly perturbed time-dependent convection-diffusion equation in one space dimension on a rectangular domain. The solution of the considered problem exhibits a boundary layer on the right side of the domain. We semi-discretize the continuous problem by means of the Crank-Nicolson finite difference method in the temporal direction. The semi-discretization yields a set of ordinary differential equations and the resulting set of ordinary differential equations is discretized by using a midpoint upwind finite difference scheme on a non-uniform mesh of Shishkin type. The resulting finite difference method is shown to be almost second-order accurate in a coarse mesh and almost first-order accurate in a fine mesh in the spatial direction. The accuracy achieved in the temporal direction is almost second order. An extensive amount of analysis has been carried out in order to prove the uniform convergence of the method. Finally we have found that the resulting method is uniformly convergent with respect to the singular perturbation parameter, i.e. ε-uniform. Some numerical experiments have been carried out to validate the proposed theoretical results.
机译：提出了一种数值方法来研究矩形域上一个空间维上的奇摄动时间相关的对流扩散方程。所考虑问题的解决方案在域的右侧具有边界层。我们通过在时间方向上的Crank-Nicolson有限差分方法对连续问题进行半离散化。半离散化产生了一组常微分方程，并且通过在Shishkin类型的非均匀网格上使用中点迎风有限差分方案离散了所得的一组常微分方程。结果表明，在空间方向上，所得的有限差分方法在粗网格中几乎是二阶精度，而在细网格中几乎是一阶精度。在时间方向上获得的精度几乎是二阶的。为了证明该方法的一致收敛，已经进行了大量的分析。最后，我们发现，相对于奇异摄动参数（即ε-均匀），所得方法是均匀收敛的。已经进行了一些数值实验以验证所提出的理论结果。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号