第三类Dirichlet边界下四阶抛物方程的紧差分格式

应用加权平均和高次Hermite插值等技术，提出逼近四阶导数的几个有用的数值微分公式，并对其截断误差进行分析。在此基础上建立求解第三类Dirichlet边界条件下四阶抛物方程初边值问题的三个高阶紧差分格式，应用Fourier分析方法证明格式的无条件稳定性，并对其进行数值验证。这三个差分格式的差异主要体现在空间导数临近边界处的离散方式不同，所得格式全局精度均达到了时间二阶、空间四阶。

Compact difference schemes for the fourth-order parabolic equations with the third Dirichlet boundary

Based on some techniques involving the weighted average and high order Hermite interpolation, several useful differentiation formulae for approximating the fourth-order derivatives are derived along with the truncation error analyses. Then three high order compact difference schemes are proposed to solve the initial-boundary value problem of the fourth-order parabolic equations with the third Dirichlet boundary conditions. The unconditional stability is proved by the Fourier analysis method. Numerical experiments are carried out. The major difference of the proposed three schemes lies in the different numerical treatment of spatial derivatives near the boundary. The global accuracy of all presented schemes can attain the order of two in time and four in space.