Construction of Runge-Kutta methods of Crouch-Grossman type of high order

@article{Jackiewicz2000ConstructionOR,
  title={Construction of Runge-Kutta methods of Crouch-Grossman type of high order},
  author={Zdzislaw Jackiewicz and Arne Marthinsen and Brynjulf Owren},
  journal={Adv. Comput. Math.},
  year={2000},
  volume={13},
  pages={405-415}
}
An approach is described to the numerical solution of order conditions for RungeKutta methods whose solutions evolve on a given manifold. This approach is based on least squares minimization using the Levenberg-Marquardt algorithm. Examples of methods of order four, ve and six are given and numerical experiments are presented which con rm that the derived methods have the expected order of accuracy. AMS subject classi cation: 65L05.