On the Starting Algorithms for Fully Implicit Runge-Kutta Methods

@article{GonzlezPinto2000OnTS,
  title={On the Starting Algorithms for Fully Implicit Runge-Kutta Methods},
  author={Severiano Gonz{\'a}lez-Pinto and Juan I. Montijano and Severiano P{\'e}rez-Rodr{\'i}guez},
  journal={BIT Numerical Mathematics},
  year={2000},
  volume={40},
  pages={685-714}
}
This paper is concerned with the behavior of starting algorithms to solve the algebraic equations of stages arising when fully implicit Runge-Kutta methods are applied to stiff initial value problems. The classical Lagrange extrapolation of the internal stages of the preceding step and some variants thereof that do not require any additional cost are analyzed. To study the order of the starting algorithms we consider three different approaches. First we analyze the classical order through the… CONTINUE READING
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