NESC0640 DE/STEP,INTRP, DEROO
DE/STE/INTRP, 1st Order Ordinary Differential Equation for Initial Value Problems
NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROBLEM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHOR, MATERIAL, CATEGORIES
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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.
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.
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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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.
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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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.
- 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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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).
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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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 |
Keywords: Adams method, initial-value problems, numerical solution, ordinary differential equations.