二阶三点数值微分公式的外推算法.pdf

21 6 Vol. 21 No. 6 2005 12 JOURNA OF TIANJIN UNIVERSITY OF TECHNO OGY D c. 2005 : 1673095X( 2005) 夏爱生, 陈博文, 胡宝安, 王 瑞, 王 强 ( , 300161) : 利用Taylor 公式, 给出了二阶三点数值微分公式在各点的截断误差的渐近展开式, 并利用 Richardson 外推算 法, 高二阶三点数值微分公式的收敛阶数, 得到高精度的二阶数值微分公式. : ; Richardson ; : O175. 5 : A The extrapolation method of twoorder and threepoint numerical differential formulas XIA Aish ng, CHEN Bow n, HU Baoan, WANG Rui, WANG Qiang ( Basic D pt. , Institut of Military Traffic, Tianjin 300161, China) Abstract: Th gradual approx imat xpansion formulas of two ord r and thr points num rical diff r ntial formula rror ar obtain d by Taylor Formula. Th conv rg nc ord r of two ord r and thr points num rical diff r ntial formula is improv d by Richardson Ex trapolation M thod. High pr cision formulas of two ord r num rical diff r ntial ar obtain d. Key words: num rical diff r ntial formula; Richardson xtrapolation m thod; two ord r and thr points formula 4 , f ( x ) C (xi , i ) , ( i = 0, 2) . 1 [ 1] : f ( x ) - 2f ( x ) + f (x ) f (x ) L ( x ) = 0 1 2 ( 1) ( ) , x 1 2 h 2 2 L 2( x ) 2 Lagrang . , O ( h )