【作者】 邢誉峰； 冯伟；

【Author】 XING Yu-Feng, FENG Wei (The Solid Mechanics Research Center, College of Aeronautics Science and Engineering, Beijing University of Aeronautics and Astronautics ,Beijing, 100083,China,)

【机构】 北京航空航天大学航空科学与工程学院固体力学研究所；

【摘要】 对线性自治系统证明了二阶、四阶李级数法分别与Runge-Kutta法中二级二阶改进Euler法和四级四阶经典R-K法的一致性;说明了李级数法和Taylor级数法的一致性,但二者计算导数的方法不同,导致不同的应用价值。分析了李级数法在求解非线性问题时的优越性。更多还原

【Abstract】 For linear autonomous system, the Lie Series algorithms of order two and order four were proved to be respectively identical with the improved Euler algorithm of stage two and order two, and with the classical R-K algorithm of stage four and order four. And the Lei Series algorithms are illustrated to be identical with Taylor progression algorithms, but they have different values of practical application because they have different calculating methods of differential coefficient. Finally, the superiority of Lie Series for approaching nonlinear system was demonstrated numerically.更多还原