Generalized Multistep Predictor-Corrector Methods

  • Authors:

  • William B. Gragg;Hans J. Stetter

  • Affiliations:

  • Bellcomm Inc., Washington, D. C.;Technische Hochschule München, Germany

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1964

Quantified Score

Hi-index 0.04

Visualization

Abstract

The order p which is obtainable with a stable k-step method in the numerical solution of y′ = f(x, y) is limited to p = k + 1 by the theorems of Dahlquist. In the present paper the customary schemes are modified by including the value of the derivative at one “nonstep point;” as usual, this value is gained from an explicit predictor. It is shown that the order of these generalized predictor-corrector methods is not subject to the above restrictions; stable k-step schemes with p = 2k + 2 have been constructed for k ≤ 4. Furthermore it is proved that methods of order p actually converge like hp uniformly in a given interval of integration. Numerical examples give some first evidence of the power of the new methods.