Cyclic composite multistep predictor-corrector methods

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.

REFERENCES

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.7 Ordinary Differential Equations
          Subjects: Multistep and multivalue methods

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.7 Ordinary Differential Equations
          Subjects: Convergence and stability

General Terms:
Theory