High Order Two-Derivative Runge-Kutta Methods with Optimized Dispersion and Dissipation Error

In this work we consider explicit Two-derivative Runge-Kutta methods of a specific type where the function f is evaluated only once at each step. New 7th order are presented with minimized dispersion and dissipation error. These two constant coefficients 5 6 stages. Also, modified phase-fitted, amplification-fitted method frequency dependent stages constructed based on Chan Tsai. The new applied to 4 well known oscillatory problems their performance compared in that Tsai.The numerical experiments show efficiency derived methods.