李级数法与Runge-Kutta法  

Lie series algorithms and Runge-Kutta algorithms

作　　者：邢誉峰[1] 冯伟[1] 

机构地区：[1]北京航空航天大学航空科学与工程学院固体力学研究所,北京100083

出　　处：《振动工程学报》2007年第5期519-522,共4页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(10772014)

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,但两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。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 he identical with Taylor progression algorithms, hut they have different values of practical application because of different calculation methods of differential coefficients. Finally, the superiority of Lie Series for approaching nonlinear system was demonstrated numerically.

关 键 词：李级数法 Runge—Kutta法 TAYLOR级数法 

分 类 号：O152.5[理学—数学]