Recent Developments in Numerical Integration

[+] Author and Article Information
J. M. Smith

Software Research Corporation, St. Louis, Mo.

J. Dyn. Sys., Meas., Control 96(1), 61-70 (Mar 01, 1974) (10 pages) doi:10.1115/1.3426777 History: Received August 09, 1973; Online July 13, 2010


Classical and even modern developments of numerical integration have not been directly concerned with the frequency-response of integration algorithms. The frequency-response characteristics of an integrator are usually presented only as a property of the integrator. When numerical integration is used in all digital (or hybrid) simulation, digital computer controlled systems or other discrete information systems, much care is given to selecting a numerical integration formula with well-behaved frequency-response characteristics. This paper is concerned with the development of a set of numerical integrators suited for application in information systems. These integrators are synthesized in such a way that they have well-defined frequency-response characteristics WHICH CAN BE VARIED; thus, each of these integrators can be tailored to integrate accurately and efficiently in many different applications. These methods of numerical integration have stability, accuracy, and noise-controlling parameters. Analytical and empirical methods of selecting the values of these parameters are discussed in detail.

Copyright © 1974 by ASME
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