Performance characteristics of higher order approximations of Runge-Kutta type are analyzed, and performance predictors for time required on machine and for error size are developed. Technique is useful in evaluating system performance, analyzing material characteristics, and designing inertial guidance and nuclear instrumentation and materials

Shanks, E. B.

English

NASA Technical Reports Server

June 1971	 Brief 71-10186 
NASA TECH BRIEF 
Marshall Space Flight Center 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage 
commercial application. Tech Briefs are available on a subscription basis from the National Technical Information 
Service, Springfield, Virginia 22151. Requests for individual copies or questions relating to the, Tech Brief program may 
be directed to the Technology Utilization Off i ce, NASA, Code KT, Washington, D. F. 20546. 
Numerical Integration of Second Order Differential Equations 
A numerical integration technique using a reduced-
step function evaluation determines approximate 
solutions to second order differential equations. The 
technique may be useful in evaluating system per-
formance, analyzing material characteristics, and 
designing inertial guidance and nuclear instrumenta-
tion and materials. 
The performance characteristics of higher order 
approximations of the Runge-Kutta type are analyzed, 
and performance predictors for the time required on 
• the machine and for the error size are developed. 
These predictors are not designed to give precise 
information; but supporting data shows that the 
information obtained provides a useful guide in 
solving the problem. 
The predictors and data indicate that the formulas 
that should be used are Shanks' formulas of the 
sixth, seventh, and eighth orders.
Note: 
Requests for further information should be directed 
to:
Technology Utilization Officer 
Code A&TS-TU 
Marshall Space Flight Center 
Huntsville, Alabama 35812 
Reference: B71-10186 
Patent status: 
No patent action is contemplated by NASA. 
Source: E. B. Shanks of

Vanderbilt University
under contract to

Marshall Space Flight Center

(MFS-20536) 
•Category 06,09 
This document was prepared under the sponsorship of the National 	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States 	 information contained in this document, or warrants that such use 
Government nor any person acting on behalf of the United States 	 will be free from privately owned.rights.
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Numerical integration of second order differential equations

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