摘要
利用一阶微商的四阶精度紧致差分逼近公式,给出了解双曲方程精度为o[(1-2θ△t,△t2+△x4)]的一种新的加权差分格式,并通过Fourier方法讨论格式的稳定性,证明了当0≤θ≤1/2时,格式是无条件稳定的;当1/2≤θ≤1时,格式是不稳定的,最后通过数值试验说明了这种方法的有效性.
Based on compact differencing formula of fourth-order accuracy for second order derivatives,a simple weighted compact finite-difference scheme with truncation o[（1-2θ△t,△t2＋/x4）]for sol-ving one-dimensional hyperbolic partial differential equations is developed. The presented method is unconditionally stable if0≤θ≤1/2, and the unstable condition is 1/2≤θ≤1.At last,a example to proof the scheme was given.
出处
《甘肃联合大学学报（自然科学版）》
2009年第4期32-33,共2页
Journal of Gansu Lianhe University :Natural Sciences
关键词
双曲方程
加权差分格式
高精度
稳定性
hyperbolic equations compact finite-difference scheme high accuracy stability
