Think globally, act locally: Solving highly-oscillatory ordinary differential equations Original Research Article

In this paper we explore the solution of highly-oscillatory differential equations, with a special reference to the linear oscillator y″+g(t)y=0, where View the MathML source. Commencing from a global-error formula, we explore the accumulation of the error by Runge–Kutta and Magnus methods. Motivated by our analysis, we present a modification of the Magnus method which results in substantially better performance.