Low-dissipation and low-dispersion fourth-order Runge–Kutta algorithm

An optimized explicit low-storage fourth-order Runge–Kutta algorithm is proposed in the present work for time integration. Dispersion and dissipation of the scheme are minimized in the Fourier space over a large range of frequencies for linear operators while enforcing a wide stability range. The scheme remains of order four with nonlinear operators thanks to the low-storage algorithm. Linear and nonlinear propagation problems are finally solved to illustrate the accuracy of the present Runge–Kutta scheme.