解抛物型方程的一类高精度显式差分格式

A Class of High Accuracy Explicit Difference Schemes for Solving the Parabolic Equations

利用待定系数法对一维抛物型方程构造了一类高精度的三层七点显式差分格式,格式的截断误差达到O(τ3+h6),稳定性条件是0<r 4/5.当r取特定值0.1335或0.5118时,格式的截断误差可提高到O(τ4+h8).

One class of high accuracy explicit difference schemes of three layers and seven points for solving one- dimension O（τ^3＋h^6）, the truncation error parabolic equations stability condition is is O （ r4 ＋ hs）. are presented by the undetermined parameters method, its truncation error is O 〈r≤4/5. When r takes the special definite value 0. 1335 or 0. 5118, itstruncation error is O（τ^4＋h^8）.