### Abstract

Two techniques for reliably controlling the defect (residual) in the numerical solution of nonstifi initial value problems were given in [D. J. Higham, SIAM J. Numer. Anal., 26(1989), pp. 1175-1183]. This work describes an alternative approach based on Hermite-Birkhofi interpolation. The new approach has two main advantages-it is applicable to Runge-Kutta schemes of any order, and it gives rise to a defect of the optimum asymptotic order of accuracy. For a particular Runge-Kutta formula the asymptotic analysis is verified numerically.

Original language | English |
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Pages (from-to) | 991-999 |

Number of pages | 8 |

Journal | SIAM Journal on Scientific Computing |

Volume | 12 |

Issue number | 5 |

Publication status | Published - 1991 |

### Keywords

- Runge–Kutta
- defect
- residual
- backward error
- Hermite–Birkhofi interpolation
- numerical mathematics

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## Cite this

Higham, D. J. (1991). Runge-Kutta defect control using Hermite-Birkhoff interpolation.

*SIAM Journal on Scientific Computing*,*12*(5), 991-999.