Exponential fitted Runge–Kutta methods of collocation type: fixed or variable knot points?

Abstract

Two different classes of exponential fitted Runge–Kutta collocation methods are considered: methods with fixed points and methods with frequency-dependent points. For both cases we have obtained extensions of the classical two-stage Gauss, RadauIIA and LobattoIIIA methods. Numerical examples reveal important differences between both approaches.