کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1703590 | 1519417 | 2013 | 13 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: New higher-order compact finite difference schemes for 1D heat conduction equations New higher-order compact finite difference schemes for 1D heat conduction equations](/preview/png/1703590.png)
In this paper, we present two higher-order compact finite difference schemes for solving one-dimensional (1D) heat conduction equations with Dirichlet and Neumann boundary conditions, respectively. In particular, we delicately adjust the location of the interior grid point that is next to the boundary so that the Dirichlet or Neumann boundary condition can be applied directly without discretization, and at the same time, the fifth or sixth-order compact finite difference approximations at the grid point can be obtained. On the other hand, an eighth-order compact finite difference approximation is employed for the spatial derivative at other interior grid points. Combined with the Crank–Nicholson finite difference method and Richardson extrapolation, the overall scheme can be unconditionally stable and provides much more accurate numerical solutions. Numerical errors and convergence rates of these two schemes are tested by two examples.
Journal: Applied Mathematical Modelling - Volume 37, Issues 16–17, 1 September 2013, Pages 7940–7952