二维抛物型方程的一族两层显式格式

A Class of Two-level Explicit Difference Schemes for Solving Two-dimensional Parabolic Equation

构造了一族二维抛物型方程的一族两层显式格式 ,当截断误差为O(Δt+Δx2 )时 ,稳定性条件为网比r =Δt/Δx2 =Δt/Δy2 ≤ 1/ 2 ,优于同类的其他显式格式 ,当截断误差为O(Δt2 +Δx4 )时成为一个简洁而实用的高精度两层显式格式 .

A class of two-level explicit difference schemes are presented for solving two-dimensional parabolic equation.When the order of truncation error is O(Δt+Δx 2),the stability condition is mesh ratio r=ΔtΔx 2=ΔtΔy 2≤12,which is better than that of all the other explicit difference schemes.And when the order of truncation error is O(Δt 2+Δx 4),it becomes a concise and practical two-level explicit scheme with high accuracy.