Solving the systems of equations arising in the discretization of some nonlinear P.D.E.'s by implicit Runge-Kutta methods
نویسندگان
چکیده
We construct and analyze iterative methods for the efficient solution of the nonlinear equations that result from the application of Implicit Runge–Kutta methods to the temporal integration of nonlinear evolution equations. Some of the schemes we consider have as starting point Newton’s method and can be applied to a large class of evolution equations. RÈSUMÈ. On construit et analyse des méthodes itératives permettant une rśolution efficace des systèmes non linéaires issus de la discrétisation en temps d’équations d’évolution non linéaires par des méthodes de Runge–Kutta implicites. Certains schémas considérés dérivent de la méthode de Newton et s’appliquent à une large classe d’équations non linéaires.
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