Parallel linear system solvers for Runge-Kutta methods

@article{Houwen1997ParallelLS,
  title={Parallel linear system solvers for Runge-Kutta methods},
  author={Piet J. van der Houwen and J. J. B. de Swart},
  journal={Adv. Comput. Math.},
  year={1997},
  volume={7},
  pages={157-181}
}
If the nonlinear systems arising in implicit Runge-Kutta methods like the Radau IIA methods are iterated by (modified) Newton, then we have to s lve linear systems whose matrix of coefficients is of the form I A⊗hJ with A the Runge-Kutta matrix and J an approximation to the Jacobian of the righthand side function of the system of differential equations. For larger systems of differential equations, the solution of these linear systems by a direct linear solver is very costly, mainly because of… CONTINUE READING
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