Optimal Runge-Kutta methods for first order pseudospectral operators (Q1306124)

Two optimal methods with respect to large stability intervals on the imaginary axis and with respect to the eigenvalue spectra of the pseudospectral discretizations are developed. Stability regions are optimized to include the outliers of the spatial operators. Performance on a model problem in computatioal aeroacoustics is evaluated. The optimized schemes have two more function evaluations per timestep than the standard fourth-order Runge-Kutta method, but allow timesteps up to 1.7 times larger. Moreover, dissipation and dispersion are reduced.