摘要
文章研究了双曲型方程的显式差分格式与隐式差分格式,并进行了数值模拟.数值实验结果表明步长比s为1/3时,两种差分格式都稳定,但显格式的计算效率高且数值解的最大误差小;步长比s为3/2时,显格式不稳定而隐格式稳定,该结论恰好与双曲型方程的显、隐格式稳定性的理论结果相一致;在步长比相同的情况下,对时间和空间区间分割越细密,数值解的最大误差越小.
The explicit and implicit difference schemes of the hyperbolic equation are studied and numerical simulation is performed.Results show that when the ratio s is 1/3,both difference schemes have stability,the explicit difference scheme exhibiting high calculation efficiency and minor maximum errors.When the ratio s reaches 3/2,the explicit difference scheme is unstable whereas the implicit scheme shows stability,which conforms to the results from the stability theory of explicit and implicit formulation of hyperbolic equations.With the same ratio,the finer segmentation between time and space interval is,the smaller the maximum error becomes.
出处
《太原师范学院学报（自然科学版）》
2014年第4期1-4,共4页
Journal of Taiyuan Normal University:Natural Science Edition
关键词
双曲型方程
显式格式
隐式格式
稳定性
计算效率
hyperbolic equation
explicit difference scheme
implicit difference scheme
stability
computational efficiency
