Series of computer subroutines integrates systems of ordinary differential equations and is used for numerical quadrature

Krogh, F. T.

English

NASA Technical Reports Server

July 1971	 Brief 71-10248 
NASA TECH BRIEF 
NASA Pasadena 0/jice 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage 
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be directed to the Technology Utilization Office, NASA, Code KT, Washington, D.C. 20546. 
Variable Order Integrators for the Numerical Solution

of Ordinary Differential Equations 
The problem:	 number of steps, the value of the independent van-
To integrate systems of ordinary differential equa-
	 able, values of dependent variables, and values of 
tions.	 user defined auxiliary functions. 
The solution: 
A series of computer subroutines which integrate 
systems of ordinary differential equations and may 
also be used for numerical quadrature. SVDQ is a 
single precision subroutine, and DVDQ is double 
precision. VODQ keeps the derivative and performs 
most of the calculations in single precision, and 
accumulates the independent and dependent variables 
in double precision. 
How it's done: 
The subroutines use linear multistep predictor-
corrector formulas of the Adams type, with formulas 
available for treating directly differential equations 
of orders 1 to 4. The subroutine automatically 
selects the integration orders (which may be dif-
ferent for different equations in the system) and the 
stepsize. The integration orders are selected so as 
to maximize the stepsize while maintaining numerical 
stability and meeting the user's requested local ac-
curacy. Special returns are available based on the
Notes: 
1. This program is written in FORTRAN IV and 
FORTRAN V for use on the IBM-7094 (IBSYS) 
computer or the UNIVAC-1108 (EXEC 8) com-
puter. 
2. Requests for further information may be directed 
to:
COSMIC 
Barrow Hall 
University of Georgia 
Athens, Georgia 30601 
Reference: B71-10248 
Patent status: 
No patent action is contemplated by NASA. 
Source: F. T. Krogh
Jet Propulsion Laboratory

under contract to

NASA Pasadena Office

(N PO- 1 1643) 
Category 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 ownedrights.
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Variable order integrators for the numerical solution of ordinary differential equations

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