当前位置: X-MOL 学术Ain Shams Eng. J. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Solution of parabolic PDEs by modified quintic B-spline Crank-Nicolson collocation method
Ain Shams Engineering Journal ( IF 6 ) Pub Date : 2020-12-04 , DOI: 10.1016/j.asej.2020.08.028
Mohammad Tamsir , Neeraj Dhiman , Amit Chauhan , Anand Chauhan

In this paper, we present a Crank-Nicolson collocation method based on modified Quintic B-splines for parabolic PDEs. The time-dependent convection–diffusion equation (CDE) and Burgers’ equation are considered. The integration of the problem is handled by using a modified quintic B-spline, over Crank-Nicolson (C-N) scheme, in space. The time-dependent terms are discretized using FDM. The efficiency as well as the accuracy of the method checked through the six numerical examples. The approximate results are presented and compared with the known exact and other numerical solutions. The Von Neumann stability is also performed.



中文翻译:

用改进的五次 B 样条 Crank-Nicolson 搭配法求解抛物线偏微分方程

在本文中,我们提出了一种基于改进的 Quintic B 样条的 Crank-Nicolson 配置方法,用于抛物线偏微分方程。考虑了与时间相关的对流扩散方程 (CDE) 和 Burgers 方程。问题的积分是通过在空间中使用 Crank-Nicolson (CN) 方案上的改进的五次 B 样条来处理的。时间相关项使用 FDM 进行离散化。通过六个算例验证了该方法的有效性和准确性。给出了近似结果,并与已知的精确解和其他数值解进行比较。还执行了冯诺依曼稳定性。

更新日期:2020-12-04
down
wechat
bug