### Abstract

Language | English |
---|---|

Pages | 991-999 |

Number of pages | 8 |

Journal | SIAM Journal on Scientific Computing |

Volume | 12 |

Issue number | 5 |

Publication status | Published - 1991 |

### Fingerprint

### Keywords

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

### Cite this

*SIAM Journal on Scientific Computing*,

*12*(5), 991-999.

}

*SIAM Journal on Scientific Computing*, vol. 12, no. 5, pp. 991-999.

**Runge-Kutta defect control using Hermite-Birkhoff interpolation.** / Higham, D.J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Runge-Kutta defect control using Hermite-Birkhoff interpolation

AU - Higham, D.J.

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

KW - Runge–Kutta

KW - defect

KW - residual

KW - backward error

KW - Hermite–Birkhofi interpolation

KW - numerical mathematics

UR - http://locus.siam.org/SISC/volume-12/art_0912053.html

M3 - Article

VL - 12

SP - 991

EP - 999

JO - SIAM Journal on Scientific Computing

T2 - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

SN - 1064-8275

IS - 5

ER -