An Efficient Integrator that Uses Gauss-Radau Spacings

  • Edgar Everhart
Part of the Astrophysics and Space Science Library book series (ASSL, volume 115)


This describes our integrator RADAU, which has been used by several groups in the U.S.A., in Italy, and in the U.S.S.R, over the past 10 years in the numerical integration of orbits and other problems involving numerical solution of systems of ordinary differential equations. First- and second-order equations are solved directly, including the general second-order case. A self-starting integrator, RADAU proceeds by sequences within which the substeps are taken at Gauss-Radau spacings. This allows rather high orders of accuracy with relatively few function evaluations. After the first sequence the information from previous sequences is used to improve the accuracy. The integrator itself chooses the next sequence size. When a 64-bit double word is available in double precision, a 15th-order version is often appropriate, and the FORTRAN code for this case is included here. RADAU is at least comparable with the best of other integrators in speed and accuracy, and it is often superior, particularly at high accuracies.


Double Precision Multistep Method Outer Planet Efficient Integrator Sequence Size 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© D. Reidel Publishing Company 1985

Authors and Affiliations

  • Edgar Everhart
    • 1
  1. 1.Physics Department and Chamberlin ObservatoryUniversity of DenverDenverUSA

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