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.
|Number of pages||8|
|Journal||SIAM Journal on Scientific Computing|
|Publication status||Published - 1991|
- backward error
- Hermite–Birkhofi interpolation
- numerical mathematics