The RK-Nystrøm Method

In “A History Of Runge Kutta Methods” (Applied Numerical Mathematics, 20, 1996, pp 247-260), J.C. Butcher presents a set of coefficients for a 5^th order RK method as derived by Kutta. The tableau is shown below:

  

However, Butcher indicates that Kutta’s 5^th order coefficients had slight errors, which were subsequently corrected by Nystrøm in 1925. The method with these coefficients are more commonly known as the RungeKutta – Nystrøm method. The tableau for the Nystrom coefficients are :

 

 The Generalized RK formulation can then be used to solve a set of ODE's.