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首页> 外文期刊>Applied Mathematical Modelling >New higher-order compact finite difference schemes for 1D heat conduction equations
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New higher-order compact finite difference schemes for 1D heat conduction equations

机译：一维热传导方程的新的高阶紧致有限差分格式

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摘要

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.
机译：在本文中，我们提出了两个高阶紧致有限差分方案，分别用Dirichlet和Neumann边界条件求解一维（1D）导热方程。特别是，我们微调调整边界附近的内部网格点的位置，以便可以直接应用Dirichlet或Neumann边界条件而无需离散化，同时使用五阶或六阶紧致有限差分近似可以在网格点处获得。另一方面，对于其他内部网格点处的空间导数，采用八阶紧凑有限差分近似。结合Crank-Nicholson有限差分法和Richardson外推法，整个方案可以是无条件稳定的，并且可以提供更为精确的数值解。通过两个例子测试了这两种方案的数值误差和收敛速度。

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