Beyond the Runge-Kutta-Wentzel-Kramers-Brillouin method

Understand

We explore higher-dimensional generalizations of the Runge-Kutta-Wentzel-Kramers-Brillouin method for integrating coupled systems of first-order ordinary differential equations with highly oscillatory solutions.

• Such methods could improve the performance and adaptability of the codes which are used to compute numerical solutions to the Einstein-Boltzmann equations.
• We test Magnus expansion-based methods on the Einstein-Boltzmann equations for a simple universe model dominated by photons with a small amount of cold dark matter.
• The Magnus expansion methods achieve an increase in run speed of about 50% compared to a standard Runge-Kutta integration method.