Optimized Runge–Kutta methods with minimal dispersion and dissipation for problems arising from computational acoustics

In this Letter a new explicit fourth-order seven-stage Runge–Kutta method with a combination of minimal dispersion and dissipation error and maximal accuracy and stability limit along the imaginary axes, is developed. This method was produced by a general function that was constructed to satisfy all the above requirements and, from which, all the existing fourth-order six-stage RK methods can be produced. The new method is more efficient than the other optimized methods, for acoustic computations.