Stiffly Accurate Runge–kutta Methods for Nonlinear Evolution Problems Governed by a Monotone Operator

@inproceedings{2010StifflyAR,
  title={Stiffly Accurate Runge–kutta Methods for Nonlinear Evolution Problems Governed by a Monotone Operator},
  author={},
  year={2010}
}
  • Published 2010
Stiffly accurate implicit Runge–Kutta methods are studied for the time discretisation of nonlinear first-order evolution equations. The equation is supposed to be governed by a time-dependent hemicontinuous operator that is (up to a shift) monotone and coercive, and fulfills a certain growth condition. It is proven that the piecewise constant as well as the piecewise linear interpolant of the time-discrete solution converges towards the exact weak solution, provided the Runge–Kutta method is… CONTINUE READING

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