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NESC0640 DE/STEP,INTRP, DEROO

DE/STE/INTRP, 1st Order Ordinary Differential Equation for Initial Value Problems

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1. NAME OR DESIGNATION OF PROGRAM:  DE/STEP,INTRP, DEROOT/STEP,INTRP.
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2. COMPUTERS
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Program name Package id Status Status date
DE/STEP/INTRP NESC0640/01 Tested 01-NOV-1977

Machines used:

Package ID Orig. computer Test computer
NESC0640/01 IBM 370 series IBM 370 series
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3. DESCRIPTION OF PROBLEM OR FUNCTION

DE/STEP,INTRP performs the solution of an initial-value problem for a system of first-order ordinary differential equations to a fixed endpoint. With the companion program, DEROOT/SETP,INTRP, the endpoint may be specified  implicitly as the root of a nonlinear function of the independent variable, the solution, and its first derivative. Each of these programs is supplied in both a basic and in a more versatile extended version.
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4. METHOD OF SOLUTION

The numerical algorithm is a variable-order, variable-step Adams method which uses a modified divided difference  representation of the PECE formulas and local extrapolation. (PECE stands for predict-evaluate-correct-evaluate). Four codes are provided: the core integrator step which advances the numerical solution of an equation one step, an interpolation routine INTRP to  interpolate the solution and its derivative at output points, a driver DE or DEROOT which simplifies using the other codes for routine problems, and a root-finding subroutine.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The basic versions are limited to the integration of a maximum of 20 equations, but the limit can be changed easily. The extended versions use variable dimensioning and have no fixed limits.
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6. TYPICAL RUNNING TIME

Less than 1 minute is required to compile and execute the sample problem.
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7. UNUSUAL FEATURES OF THE PROGRAM

The codes emphasize efficiency in  terms of function evaluations, flexibility in the integration, and ease of use. They detect and deal with discontinuities and moderate  stiffness, warn the user of severe stiffness, detect requests for too much accuracy, and are essentially independent of the number and placement of output points. The codes are written in single- precision; instructions for converting them to double-precision are  included in the reference reports.
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8. RELATED AND AUXILIARY PROGRAMS

Subroutine MACHIN, used to determine the machine-dependent roundoff error, is included.
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9. STATUS
Package ID Status date Status
NESC0640/01 01-NOV-1977 Tested at NEADB
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10. REFERENCES

- L.F. Shampine and M.K. Gordon,
  Using DE/STEP,INTRP to Solve Ordinary Differential Equations,
  SLA Memorandum, July 1974.
- M.K. Gordon,
  Using DEROOT/STEP,INTRP to Solve Ordinary Differential Equations,
  SAND-75-0211, April 1975.
- L.F. Shampine and M.K. Gordon,
  Computer Solution of Ordinary Differential Equations: The Initial
  Value Problem,
  W.H. Freeman and Company, San Francisco, 1975.
- DE/STEP,INTRP, ACC No. 64 0.6600D, ACC Programming Note 75-8,
  November 19, 1974, Revised February 26, 1976.
- DE/STEP,INTRP, ACC No. 640.360D, ACC Programing 75-9, November 19,   1974, Revised February 26, 1976.
- G.D. Byrne and A.C. Hindmarsh,
  An Annotated List of ODE System Solvers,
  National Energy Software Center Note 81-71, August 13, 1981.
- DE/STEP,INTRP, ACC No. 640.360D, 640.6600D, ACC Author Note 76-23,   February 26, 1976.
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11. MACHINE REQUIREMENTS

For execution of the basic version: 44K bytes (IBM360), 12000 (octal) words (CDC6600).
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NESC0640/01 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED

OS/360 (IBM360),  SCOPE 3.3 (CDC6600), SCOPE 2.1.3 (CDC7600).
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

The
programs are expected to be machine-independent. However, subroutines DE, DEROOT, and STEP store several variables internally  between calls; this ability is not guaranteed in Standard FORTRAN. The extended versions do not assume internal storage, but are unacceptable to the WATFIV compiler (and possibly to others).
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15. NAME AND ESTABLISHMENT OF AUTHOR

L.F. Shampine and M.K. Gordon
Sandia Laboratories
P.O. Box 5800
Albuquerque, New Mexico 87115
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16. MATERIAL AVAILABLE
NESC0640/01
File name File description Records
NESC0640_01.002 DE/STEP/INTRP (BASIC) SOURCE F4 EBCDIC 760
NESC0640_01.003 DE/STEP/INTRP (BASIC) DEMONSTR.PROG. F4 28
NESC0640_01.004 DE/STEP/INTRP (EXTENDED) SOURCE F4 819
NESC0640_01.005 DE/STEP/INTRP (EXTENDED) DEMONSTR.PROG. F4 30
NESC0640_01.006 DEROOT/STEP/INTRP(BASIC) SOURCE F4 1035
NESC0640_01.007 DEROOT/STEP/INTRP(BASIC) DEMONSTR.PROG. 32
NESC0640_01.008 DEROOT/STEP/INTRP(EXTENDED) SOURCE F4 1091
NESC0640_01.009 DEROOT/STEP/INTRP(EXTENDED) DEMONSTR.PROG. 33
NESC0640_01.010 AUX.PROGRAMS MAIN, MACHIN (F4, EBCDIC) 24
NESC0640_01.011 DE/STEP/INTRP(BASIC&EXTENDED) PRINTOUT 4
NESC0640_01.012 DEROOT/STEP/INTRP(BASIC&EXTENDED) PRINTOUT 11
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17. CATEGORIES
  • P. General Mathematical and Computing System Routines

Keywords: Adams method, initial-value problems, numerical solution, ordinary differential equations.