摘要
将文献[1]的高阶差分算法推广到变系数抛物型方程的情形.首先综合应用降维降阶法建立了变系数抛物型方程的一个不需要用到u在边界上的二阶导数的值、计算量小、精度高的有限差分格式,所得差分格式具有O(2τ+h4)阶精度,并给出了该差分格式的截断误差的表达式;然后通过引进过渡层导出了近似因式分解的交替方向隐差分格式的算法.
This article extends the high--order difference algorithm of article [1] to variable coefficient parabolic equation. Firstly, we comprehensively apply the method of reduction of order and the method of redution to construct limited difference scheme of variable coefficient parabolic equation,not using the second derivative value of u on its boundary, which has O（τ^2 ＋h^4） --ORDER ACCUTACY. Additionally, the difference scheme expressions of truncation error is presented. Secondly, the algorithm of ADI（alternate direct implicit）difference scheme of approximate polynomials factorization is presented by introducing a variable of intermediate value.
出处
《兰州工业高等专科学校学报》
2009年第2期44-47,共4页
Journal of Lanzhou Higher Polytechnical College
关键词
变系数
抛物型方程
高阶
差分格式
算法
variable coefficient parabolic equation
higher-- order
difference scheme
algorithm
