四维热传导方程的一族两层显格式

A Class of Two-level Explicit Difference Schemes for Solving 4-D Heat Equation

构造了解四维热传导方程的一族两层显格式,证明了当截断误差为O(△t+△x2)时,其稳定性条件为网比r=△t/△x2=△t/△y2=△t/△z2=△t／△w2≤11／24优于同类的其他显格式,当截断误差阶为O(△t2+△x4)时,此格式为一个简洁而实用的高精度两层显格式。

A class of two-level explicit difference schemes for solving 4-D heat equation are presented, when the order of trunction error is O（△t＋△x^2）, the stability condition is the mash ratio r=△t/△x^2=△t/△y^2=△t/△z^2=△t/△w^2≤11/24, which is better than that of all other explicit difference schemes. When the order of trunction error is O（△t^2＋△x^4）, it becomes a concise and practical explicit schemes of two level with high accuracy.