Compensating for order variation in mesh refinement for direct transcription methods II: computational experience

Authors:
J. T. Betts;N. Biehn;S. L. Campbell;W. P. Huffman
Affiliations:
Mathematics and Engineering Analysis, The Boeing Company, P.O. Box 3707, MS 7L-21, Seattle, WA;Operations Research Program, North Carolina State University, Raleigh, NC;College of Physical and Mathematical Science, Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC;Mathematics and Engineering Analysis, The Boeing Company, P.O. Box 3707, MS 7L-21, Seattle, WA
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

Citing 3
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Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
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Compensating for order variation in mesh refinement for direct transcription methods

Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations

Direct transcription solution of high index optimal control problems and regular Euler-Lagrange equations

Journal of Computational and Applied Mathematics

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Abstract

The numerical theory for Implicit Runge Kutta methods shows that there can be order reduction when these methods are applied to either stiff or differential algebraic equations. A previous paper introduced a way to try and compensate for this order reduction in designing mesh refinement strategies. This paper presents the results from a number of computational studies on the effectiveness of this approach. In addition, we present a new test problem which can be used to examine the efficiency of codes developed for a particular class of applications.