Modified two-derivative Runge-Kutta methods for solving oscillatory problems

In this work we consider modified Two Derivative Runge-Kutta methods for initial value problems with periodic or oscillatory behavior. The coefficients of the new methods depend on the frequency of each problem so that the harmonic oscillator y′′=−w 2 y is integrated exactly. We modify two methods of algebraic order five with three stages. Numerical results will be given for three oscillatory problems.