NESC9918 DASSL.

DASSL, Solution of Differential Algebraic Equation

NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROGRAM 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 AUTHORS, MATERIAL, CATEGORIES

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1. NAME OR DESIGNATION OF PROGRAM: DASSL.

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2. COMPUTERS

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Program name	Package id	Status	Status date
DASSL	NESC9918/02	Tested	01-DEC-1993

Machines used:

Package ID	Orig. computer	Test computer
NESC9918/02	Many Computers	DEC VAX 6000

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3. DESCRIPTION OF PROGRAM OR FUNCTION

DASSL is designed for the numerical solution of implicit systems of differential/algebraic equations written in the form F(t,y,y')=0, where F, y, and y' are vectors, and initial values for y and y' are given. Systems of differential/algebraic equations (DAE) arise in several diverse applications in the physical world. Problems of this type occur frequently in the numerical method-of-lines treatment of partial differential equations, in the simulation of electronic circuits, where they are sometimes called semistate equations, and in the dynamic analysis of mechanical systems. These problems can all be solved using DASSL. Both a single-precision version (SDASSL) for long word-length machines and a double-precision version (DDASSL) for short word-length machines are included.

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4. METHOD OF SOLUTION

The derivatives y' are approximated by backward differentiation formulae (BDF), and the resulting nonlinear system at each time-step is solved by Newton's method.

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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM:

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6. TYPICAL RUNNING TIME:

NESC9918/02

NEA-DB executed the demonstration program on a DEC VAX 600-510 computer in less than 1 CPU second for the single- precision version and in 1.24 CPU seconds for the double-precision version.

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7. UNUSUAL FEATURES OF THE PROGRAM:

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8. RELATED AND AUXILIARY PROGRAMS

The linear systems are solved using routines from the LINPACK (NESC 800) subroutine package. Error handling is accomplished using routines from the SLATEC (NESC 820) common mathematical library package.

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9. STATUS

Package ID	Status date	Status
NESC9918/02	01-DEC-1993	Tested at NEADB

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10. REFERENCES

- K.E. Breman, S.L. Campbell, and L.R. Petzold:
  Numerical Solution of Initial-Value Problems in Differential-
  Algebraic Equations, Elsevier Science Publishing Company,
  New York (1989).

NESC9918/02, included references:

- Linda R. Petzold:
  A Description of DASSL: A Differential/Algebraic System Solver
  SAND82-8637 (September 1982).
- L. Eyberger:
  DASSL Tape Description and Implementation Information
  NESC Note 92-24 (November 13, 1991).
- NEA Data Bank:
  Graphical Comparison of the Accuracy of the SINGLE and DOUBLE
  Precision Versions of DASSL on the DEC VAX 6000-510
  NEADB 03/11/93

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11. MACHINE REQUIREMENTS:

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12. PROGRAMMING LANGUAGE(S) USED

Package ID	Computer language
NESC9918/02	FORTRAN-77

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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:

NESC9918/02

VMS 5.5-2 (VAX 6000).

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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:

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15. NAME AND ESTABLISHMENT OF AUTHORS

        L.R. Petzold*
        Computation and Mathematics Research Division
        Lawrence Livermore National Laboratory
*Present address - University of Minnesota

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16. MATERIAL AVAILABLE

NESC9918/02

File name	File description	Records
NESC9918_02.001	DASSL Information file	186
NESC9918_02.002	SDASSL Source code file # 1	213
NESC9918_02.003	SDASSL Source code file # 2	702
NESC9918_02.004	SDASSL Source code file # 3	2549
NESC9918_02.005	SDASSL Source code file # 4	143
NESC9918_02.006	SDASSL Installation file	26
NESC9918_02.007	SDASSL output file (for two test problems)	118
NESC9918_02.008	DDASSL source code file # 1	219
NESC9918_02.009	DDASSL source code file # 2	702
NESC9918_02.010	DDASSL source code file # 3	2550
NESC9918_02.011	DDASSL source code file # 4	143
NESC9918_02.012	DDASSL Installation file	27
NESC9918_02.013	DDASSL Output file (for two test problems)	113

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17. CATEGORIES

P. General Mathematical and Computing System Routines

Keywords: differential equations, finite difference method, nonlinear problems, numerical solution, ordinary differential equations.