解多维抛物型方程的两个三层显格式

Two Classes of Explicit Schemes for Solving Multi-Dimensional Parabolic Equations

提出两类解Ｎ－维抛物型方程的两个三层显式差分格式．显式格式（Ⅰ）的稳定性条件是，且，其中Ｐ＝１，２，…，Ｎ．而显式格式（Ⅱ）当参数α＞１时是无条件稳定的．它们的局部截断误差阶分别是及。

Two classes of explicit three-level difference schemes are derived for solving parabolic partial differential equation of N-dimension.Explicit scheme Ⅰ is stable under the condition of and where rp=△t/(△rp)2, (p=1,2,..,N);while explicit scheme Ⅱ is unconditionally stable in caseparameter α≥1.Their respective local truncation error are and.