Generation of high-order interpolants for explicit Runge-Kutta pairs

ABSTRACT

Explicit Runge-Kutta pairs can be enhanced by providing them with interpolants. Enhancements include the ability to estimate and control the defect, to produce dense output, and to calculate past values in delay differential equations. The coefficients of an interpolant are easily generated by bootstripping on the order conditions. However, the generation of high-order interpolants requires a large number of arithmetic operations. We describe an efficient algorithm for the generation of high-order interpolants and illustrate the use of the algorithm with three applications.

REFERENCES

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on matrices

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

General Terms:
Algorithms

Keywords:
Runge-Kutta, explicit, generation, high order interpolants, pairs