Dormand–Prince method

More specifically, it uses six function evaluations to calculate fourth- and fifth-order accurate solutions.

This error estimate is very convenient for adaptive stepsize integration algorithms.

Dormand and Prince chose the coefficients of their method to minimize the error of the fifth-order solution.

This is the main difference with the Fehlberg method, which was constructed so that the fourth-order solution has a small error.

For this reason, the Dormand–Prince method is more suitable when the higher-order solution is used to continue the integration, a practice known as local extrapolation.