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 |
|---|---|
| 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
Fingerprint Dive into the research topics of 'Runge-Kutta defect control using Hermite-Birkhoff interpolation'. Together they form a unique fingerprint.
Cite this
Higham, D. J. (1991). Runge-Kutta defect control using Hermite-Birkhoff interpolation. SIAM Journal on Scientific Computing, 12(5), 991-999.