Explicit fifth order Runge-Kutta methods with five stages for quadratic ODEs
It is well-known that there exist no general purpose explicit fifth order five stage Runge-Kutta methods. One may however wonder whether there exist explicit five stage methods which are of fifth order for special kinds of problems, for instance problems y′=f(x, y) where f is an m dimensional vector of polynomials of degree at most d in each of the arguments. It is shown that there exist explicit five stage Runge-Kutta methods for quadratic ODEs (d=2). Solutions are given for the non-confluent case and a numerical example is incorporated.
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