A New Recurrence for Computing Runge–Kutta Truncation Error Coefficients

Researchers investigating Runge–Kutta methods use truncation error coefficients to derive formulas and assess their quality. In this paper Albrecht’s recurrence for generating order conditions is refined to produce truncation error coefficients. The refined recurrence provides a fast and relatively simple way of calculating truncation error coefficients of the Albrecht expansion for general Runge–Kutta methods.