A block 6(4) Runge-Kutta formula for nonstiff initial value problems

ABSTRACT

A new selection is made for an efficient two-step block Runge-Kutta formula of order 6. The new formula is developed using some of the efficiency criteria recently investigated by Shampine, and as a result, a block formula with much improved performance is obtained. An important property of this new formula is that there is a “natural” interpolating polynomial available. This can be used to compute approximate solution values at off-step points without the need to compute any additional function evaluations. The quality of this interpolant is examined, and it is shown to have certain desirable properties. The performance of the new block Runge-Kutta formula is evaluated using the DETEST test set and is shown to be more efficient than certain other standard Runge-Kutta formulas for this particular test set.

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.7 Ordinary Differential Equations
          Subjects: Initial value problems

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.1 Interpolation
          Subjects: Interpolation formulas

General Terms:
Algorithms, Performance, Theory