Some recent research on Runge-Kutta methods
The study of Runge-Kutta methods has been a very active field of research since the work of C. Runge (1895), K. Heun (1900) and W. Kutta (1901). Nowadays, this class of methods has become a fundamental tool in the practical solution of differential equations and it is present in the most used packages of software. One can think that there is no much else to study in relation with RK formulas but however, the development of new hardware and software technologies that provide more powerful capabilities of computation, and the numerical simulation of every time more complex real life problems lead to new requirements to the numerical integrators that demand further research. As an example we will consider some current problems, such as those arising in computational aeroacoustic, and we will see how the research on RK methods can contribute to improve their numerical simulation.
