Cash-Karp method

The Cash-Karp method is a numerical method for solving ordinary differential equations, proposed by Professor Jeff R. Cash of Imperial College London and Alan H. Karp of the IBM Scientific Center. It is a member of the Runge-Kutta family of ODE solvers. More specifically, it uses six function evaluations to calculate both a fourth-order and a fifth-order accurate solution, and the difference between the two is taken as the error estimate of the fourth-order solution. That estimate is very convenient for adaptive stepsize integration algorithms, which shrink or grow the step as the error demands. Similar embedded integration methods include the Fehlberg (RKF) and Dormand-Prince (RKDP) methods.