求解初值问题的指数拟合RKNd方法(英文)  

Exponentially Fitted RKNd Methods for Solving Oscillatory ODEs

作　　者：翟文娟[1] 陈丙振[1] 

机构地区：[1]北京交通大学海滨学院数学部,沧州河北061100

出　　处：《数学进展》2013年第3期393-404,共12页Advances in Mathematics（China）

摘　　要：本文给出了求解初值问题的指数拟合的RKNd方法.此类方法对于解可以表示为函数{exp(λt),exp(-λt)},λ∈C,或{sin(ωt),cos(ωt)},其中λ=iω,ω∈R之线性组合的微分方程精确成立.数值试验表明,指数拟合RKNd方法的计算效率要优于指数拟合RK方法和RKNd方法.In this paper, we derive the exponentially fitted RKNd methods for solving oscillatory ODEs. The new methods integrate exactly differential systems whose solutions can be expressed as linear combinations of functions from the Set {exp（λt）,exp（-λt）}, λ∈C, or equivalently, {sin（ωt）,cos（ωt）} when λ = iω, ω∈R. Numerical experiments are accompanied to show the efficiency and competence of the exponentially fitted RKNd methods compared with some exponentially fitted RK methods and RKNd methods.

关 键 词：RKNd方法 指数拟合 稳定性 耗散 效率 振荡 

分 类 号：O241.81[理学—计算数学]