一类加权半隐格式增量未知元方法的稳定性和误差估计  

ON STABILITY AND ERROR ESTIMAES FOR A CLASS OF WEIGHTED SEMI-IMPLICIT SCHEMES OF THE INCREMENTAL UNKNOWNS METHODS

作　　者：黄建清 伍渝江[1] 

机构地区：[1]兰州大学数学与统计学院

出　　处：《计算数学》2005年第2期183-198,共16页Mathematica Numerica Sinica

基　　金：数学天元基金项目(A0324649)资助教育部高校骨干教师基金(GG-110-73001-1014)资助甘肃省自然科 学基金(3ZS041-A25-011)资助.

摘　　要：本文提出一类基于一维热传导方程数值求解的增量未知元方法加权半隐格式,并由此给出分析稳定性和整体截断误差的新方法.我们引入源于Laplace算子的两组基底,使得放大矩阵易于分析;我们利用IU性质和矩阵运算技巧,严格证明了所述加权格式的稳定性充分条件和全局误差估计,这些结果本质上优于1/4≤θ≤3/4条件下的常见情形.所得结论为恢复初始误差带来可能,为选择最优加权半隐格式提供了理论依据.A class of weighted semi-implicit difference schemes based on Incremental Unknowns (IU) are proposed for solving one-dimensional heat conduction equation, upon which we then present a new method to analyze the stability and global error. For that purpose, we introduce two important bases stemming from the eigenvectors of the Laplace operator, in which the amplification matrix is easy to analyze. Making use of IU properties and matrix techniques, we prove rigorously the sufficient stability conditions and the global error estimates of these schemes which show essentially better than the necessary stability condition of the usual semi-implicit schemes under the condition of 1/4≤θ≤3/4. It is also possible for one to recover the initial errors of the schemes under the condition of the Theorem 5.1. Besides, the results in Theorems 4.4 and 5.1 show us how to obtain the optimal factor of our weighted semi-implicit schemes with higher accuracy.

关 键 词：误差估计 稳定性 隐格式 增量 LAPLACE算子 整体截断误差 热传导方程 数值求解 运算技巧 充分条件 最优加权 U性质 误差带 矩阵 一维 

分 类 号：O241[理学—计算数学]