摘要
利用加耗散项的方法,通过选取适当参数,构造二维抛物型方程的若干两层显式差分格式.其局部截断误差阶为O(τ+h2),而稳定性条件最好为r=(ΔΔxt)2=(ΔΔyt)2=hτ2≤1,优于(或不亚于)其他两层显格式,且这些格式都是简洁实用的两层显格式.数值试验表明,所做的稳定性分析是正确的.
By introducing dissipative term into conventional explicit schemes and choosing apropos parameter, several two-level explicit difference schemes are established for solving the equation of two-dimensional parabolic type. The order of the local discretization is O（ι＋h^2 ） and best stability condition is r=Δt/（Δx）^2=Δt/（Δy）^2=τ/h^2≤1 which is better than （or equal to） the order by other two level explicit schemes. The schemes are also simple and practical explicit two-level difference schemes. The stability analysis made by the author is clearly stabled by numerical example.
出处
《华侨大学学报（自然科学版）》
CAS
北大核心
2008年第4期622-626,共5页
Journal of Huaqiao University(Natural Science)
基金
国务院侨务办公室科研基金资助项目(04QZR09)
关键词
二维抛物型方程
两层显式差分格式
耗散项
稳定性
收敛性
equation of two-dimensional parabolic type
two-level explicit difference scheme
dissipative term
stability
convergence
