欧拉方法整体截断误差限的计算  

THE CALCULATION OF THE GLOBAL TRUNCATION ERROR BOUNDS OF EULER METHOD

作　　者：种兰祥[1] 张万绪[1] 宋永明 

机构地区：[1]西北大学电子科学系,陕西西安710069 [2]陕西地矿局物化探队,陕西西安710055

出　　处：《计算机应用与软件》2006年第3期137-138,共2页Computer Applications and Software

基　　金：陕西省地矿局资助项目(UE0302)

摘　　要：从理论上推导出了欧拉方法的整体截断误差的上限公式和下限公式,作一定的近似后,得到的整体截断误差上限公式就变为现用的整体截断误差上限公式。数值计算结果证明,推导出的整体截断误差上限公式的准确度明显高于现用整体截断误差上限公式的准确度。因此,应该用推导出的公式代替现用公式。Both upper bound formula and lower bound formula of the global truncation error of Euler method have been derived theoretically. After making certain approximate processing, the derived upper formula changes into current upper bound formula. Numeric calculation results show that the accuracy of the derived upper bound formula is obviously higher than current upper bound formula. So, current upper bound formula can be perfectly replaced by derived upper bound formula.

关 键 词：欧拉方法 整体截断误差 局部截断误差 初值问题 

分 类 号：O241.81[理学—计算数学] O241.8[理学—数学]