Block 6(5) and 7(6) explicit Runge—Kutta formulae Original Research Article

A general approach to the derivation of block two-step explicit Runge—Kutta formulae of orders 6(5) and 7(6) is described. A major advantage offered by this approach is that it allows the construction of a free interpolant which can be used to approximate the solution at “off-step” points. Two particular block formulae from these general classes are given and shown theoretically to be competitive with standard Runge—Kutta formulae. The result of extensive numerical testing to support this theory is also given.