五维热传导方程的一族两层显格式

A class of two-level explicit difference scheme for solving 5-D heat equation

构造了五维热传导方程的一族两层显格式,证明了当截断误差阶为O(τ+h2)时,其稳定性条件为网比r=hτ2≤21,优于同类的其它显格式,当截断误差阶为O(τ2+h2)时,可以得到一个简洁而实用的二阶精度的两层显格式.

A class of two-level explicit difference schemes for solving 5-D heat equation are presented,when the order of trunction error is O（τ ＋ h2）,the stability condition is the mash ratio r = hτ2 ≤ 21,which is better than that of all other explicit difference shcemes.When the order of trunction error is O（τ2 ＋ h2）,it becomes a concise and practical explicit schemes of two level with two-order accuracy.