求解初值问题的指数拟合RKNd方法

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 method.s.