四维抛物型方程的高精度分支稳定的显式差分格式

High-order accuracy explicit difference schemes with branching stability for solving four-dimension parabolic equation

对四维抛物型方程构造了一个高精度显格式,格式的稳定性条件为r=Δt/Δx^2=Δt/Δy^2=Δt/Δz^2=Δt/Δw^2<1/2,截断误差阶达到O(Δt^2+Δx^4),通过数值实验,表明本文理论分析的正确性和文中格式较同类格式的优越性.

High-order accuracy explicit difference schemes with branding stability for solving four-dimension parabolic equation is constructed. The stability condition is r=Δt/Δx^2=Δt/Δy^2=Δt/Δz^2=Δt/Δw^2〈1/2 and the truncation error is O（Δt^2＋Δx^4） . Finally some numerical results are presented to show the advantage of the schemes.