Equation Chapter 1 Section 1 Implicit Exponentially Fitted RKNd Methods for Solving Oscillatory ODEs

Abstract

In this paper, we derive the implicit 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 when λ = iω, ω ∈ R. Numerical experiments are accompanied to show the efficiency and competence of the implicit exponentially fitted RKNd methods compared with implicit RKNd methods.