# 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} }

- Published 2000
DOI:10.1023/A:1022340401909

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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SHOWING 1-10 OF 17 REFERENCES

## Solving Ordinary Differential Equations II

VIEW 6 EXCERPTS

HIGHLY INFLUENTIAL

## IRK methods for DAE: starting algorithms

VIEW 1 EXCERPT

## Construction of starting algorithms for the RK-Gauss methods

VIEW 2 EXCERPTS

## Starting algorithms for IRK methods

VIEW 2 EXCERPTS

## Runge-Kutta methods for linear problems

VIEW 1 EXCERPT

## S

## Ch

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