Exponential fitted Gauss, Radau and Lobatto methods of low order (Q937185)

The authors construct a set of so-called exponential fitted Runge-Kutta methods. The idea is to use the nodes of a classical \(s\)-stage Runge-Kutta method (e.g., a Gauss, Radau or Lobatto method) and to choose the weights such that the methods are exact for linear combinations of the functions \(1\), \(x\), \(x^2, \dots, x^{s-1}\) and \(\exp(\lambda x)\) for a suitably chosen \(\lambda\). A consistency analysis is provided as well as an investigation of the regions of absolute stability for some important special cases. Numerical examples indicate that the methods work well for stiff differential equations.