摘要
针对色散方程u/t=a3u/x3,a为常数的初边值问题,采用组合差商法,构造了两组互为对称带参数的三层四点显式差分格式.格式的局部截断误差阶为O(τ2+h4),稳定性条件为0<|r|≤1/4.当其中的参数满足一定的条件后,格式的精确度可以提高到O(τ2+h6),稳定性条件为0<|r|≤1/60.这是两组高精度差分格式.最后用数值例子验证了理论分析的正确性.
For solving the initial boundary value problem of the dispersive equation ut=auxxx,two groups of symmetrical explicit schemes were designed by combining difference solution.They were containing parameters and three-level with four net points in the middle level.Their truncation errors were O(τ^2+h^4)and stability conditions were 0|r|≤1/4.When the parameters satisfied some relation,the precise of the schemes could be improved to O(τ^2+h^6).At this time,the stability conditions were 0〈|r|≤1/60.The precise of these schemes were high.The last numerical example proves the theoretical analysis is correct.
出处
《江苏科技大学学报(自然科学版)》
CAS
北大核心
2010年第4期395-399,共5页
Journal of Jiangsu University of Science and Technology:Natural Science Edition
基金
国家自然科学基金资助项目(40904034)
四川省高校重点实验室开放基金资助项目(SCSXDZ2009016)
关键词
色散方程
组合差商法
显格式
高精度
稳定性
dispersive equation
combined difference solution
explicit scheme
high precise
stability