Cyclic composite multistep predictor-corrector methods

  • Authors:

  • Eldon Hansen

  • Affiliations:

  • -

  • Venue:
  • ACM '69 Proceedings of the 1969 24th national conference
  • Year:
  • 1969

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Abstract

Multistep predictor-corrector methods are commonly used for the numerical solution of ordinary differential equations. In its simplest form a k-step method with accuracy of order exceeding k + 2 is unstable. Methods such as those of Gragg and Stetter and of Butcher obtain high accuracy while retaining stability. However, the price paid is additional evaluation(s) of the function f(x,y) occurring in the differential equation y' &equil; f(x,y). In this paper, we consider composite methods using M different correctors applied cyclically. We show that a composite method with accuracy of 2k - 1 can be stable and entails no additional computation.