摘要
结合预报校正线性多步法与高阶紧致差分格式方法的优点,空间导数采用四阶紧致差分格式进行离散之后,对得到的空间半离散格式采用改进的预报校正的线性多步法进行时间推进,得到一种时空方向均为四阶精度的求解非线性对流扩散方程的高精度方法。数值试验表明该格式可以有效求解非线性对流扩散方程,验证了格式的良好性能。
A high-order compact schemes is derived for the nonlinear convection diffusion equation by solving the non-linear algebraic equations. The spatial derivatives are discretized by fourth-order compact finite scheme. The spatial semi-discretized equations is solved by a fourth-step predictor-corrector linear mutistep method in time. The truncation error of the new scheme reaches 0（T4 ＋ h4） . Its excellent properties are proved by numerical exam- inations. The results show that the scheme is good with the exact solutions.
出处
《科学技术与工程》
北大核心
2013年第13期3686-3690,共5页
Science Technology and Engineering
基金
国家自然科学基金项目(10961002)
北方民族大学自主科研项目(2011ZQY026)资助
关键词
紧致差分格式
预报校正
线性多步法
非线性对流扩散方程
compact finite difference predictor-corrector linear multi-step nonlinear convection diffusion reaction equation
