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- 2018
求解一维扩散反应方程的隐式高精度紧致差分格式
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Abstract:
提出了一维扩散反应方程的一种隐式高精度紧致差分格式，空间二阶导数采用四阶紧致差分格式进行离散，时间导数采用四阶向后欧拉公式进行离散，格式截断误差为Ο（τ4+h4），即时间和空间都可以达到四阶精度，最后通过数值实验验证了本文方法的精确性和可靠性.
In this paper, an implicit high accuracy compact difference scheme for solving the one-dimensional reaction-diffusion equation is proposed. The fourth-order compact difference scheme is adopted to discretize the second derivative in space, while the fourth-order backward Euler formula is used for discretization of time derivative. The truncation error of this scheme is Ο(τ4+h4), i.e, it is the fourth-order accuracy in both time and space. The accuracy and reliability of the present scheme is validated by some numerical experiments
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