Stepsize selection for ordinary differential equations

Authors:
Fred T. Krogh
Affiliations:
Math à la Carte, Inc., Tujunga, CA
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
2010

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Abstract

This note offers a new approach based on a least squares fit to past data in order to select the stepsize when solving an ordinary differential equation. The approach used may have applicability to other situations where one wants to repeatedly make short term predictions given somewhat noisy data. Additional ad hoc rules help significantly for reliability and efficiency. Comparisons with some Runge-Kutta codes, an Adams code, and an extrapolation code are also included.