解抛物型方程的一族六点隐式差分格式

A class of implicit difference schemes of six points for solving the parabolic equations

提出了求解一维抛物型方程的一族两层六点隐式格式.格式的截断误差为O(τ2+h4).利用Fourier方法证明了差分格式当1/2≤θ≤1时,格式绝对稳定;当0≤θ<1/2时,只有r≤1/6(1-2θ),格式才是稳定的.数值试验表明,该族格式是有效的,且理论分析与实际计算相吻合.

Proposed in the paper was a class of two-level implicit difference schemes for solving one- dimension parabolic equation. The truncation error of the scheme was O （R^2 ＋ h^4） By Fourier method, the difference scheme was proved to be unconditionally stable if 1/2 ≤ 0 ≤ 1, and the stability condition was 0 〈 r ≤ 1/6（1 - 2θ） while 0 ≤ θ 〈 1/2. The numerical experiment showed the difference scheme was effective and theoretical analysis of them coincides with practical calculation of them.