Exponentially fitted two-step Runge–Kutta methods: Construction and parameter selection

We derive exponentially fitted two-step Runge–Kutta methods for the numerical solution of y′=f(x,y)y′=f(x,y), specially tuned to the behaviour of the solution. Such methods have nonconstant coefficients which depend on a parameter to be suitably estimated. The construction of the methods is shown and a strategy of parameter selection is presented. Some numerical experiments are provided to confirm the theoretical expectations.