【摘要】 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。更多还原

【Abstract】 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 +△x2), the stability condition is the mash ratio r =△t/△x2 =△t/△y2 =△t/△z2 =△t /△w2≤11/24, which is better than that of all other explicit difference schemes. When the order of trunction error is O(△t2 +△x4), it becomes a concise and practical explicit schemes of two level with high accuracy.更多还原