A curiosity of low-order explicit Runge-Kutta methods

J. Oliver
1975 Mathematics of Computation  
By introducing an additional parameter into the first stage of the explicit Runge-Kutta process, new formulae of second and third order are derived, offering improved error bounds in the second-order case.
doi:10.1090/s0025-5718-1975-0391514-5 fatcat:5rlzhzordvhhfmzm666xjkmfmi