Initial Value Routines in the NAG Library

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Initial Value Routines in the NAG Library

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 5 , Issue 4 (December 1979) table of contents

Pages: 386 - 400

Year of Publication: 1979

ISSN:0098-3500

Author

Ian Gladwell

Department of Mathematics, University of Manchester, Manchester M13 9PL, England

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 9, Downloads (12 Months): 39, Citation Count: 6

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references cited by index terms collaborative colleagues

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	J. C. P. Bus , T. J. Dekker, Two Efficient Algorithms with Guaranteed Convergence for Finding a Zero of a Function, ACM Transactions on Mathematical Software (TOMS), v.1 n.4, p.330-345, Dec. 1975 [doi>10.1145/355656.355659]
	2	CRAIGIE, J.A.I. A variable order multlstep method for the numerical solution of stiff systems of ordinary differential equations. NA Rep. 11, Dep. of Mathematics, U. of Manchester, England, 1975.
	3	DUFF, I. MA28--a set of Fortran subroutines for sparse unsymmetnc linear equations. AERE Rep R. 8730, HMSO, London, 1977.
	4	ENRIGHT, W.H., BEDET, R., FARKAS, I., AND HULL, T.E. Test results on initial value methods for non-stiff ordinary differential equations. Rep. 68, Dep. of Comptr. Sci., U. of Toronto, Canada, 1974.
	5	ENRIGHT, W.H., HULL, T. E., AND LINDBERG, B. Comparing numerical methods for stiff systems of ODE's. BIT 15 (1975), 10-48.
	6	GLADWELL, I. On the ordinary differential equation initial value routines in the NAG library. NA Rep. 38, Dep. of Mathematics, U. of Manchester, England, 1979.
	7	GLADWELL, I. The development of the boundary value codes in the ordinary differential equations chapter of the NAG library. NA Rep. 30, Dep. of Mathematics, U. of Manchester, England, 1978. To be pubhshed in modified form.
	8	GLADWELL, I., CRAIGIE, J.A.I., AND CROWTHER, C.R. Testing initial-value problem subroutines as black boxes. NA Rep. 34, Dep. of Mathematics, U. of Manchester, England, 1979.
	9	HINDMARSH, A.C. A tentatzve user interface standard for ODEPACK. Rep. UCID-17954, Lawrence Llvermore Lab., Livermore, Calif., 1978.
	10	HINDMARSH, A.C. GEAR: Ordinary dafferentlal equation solver. Rep. UCID-30001, Rev. 3, Lawrence Llvermore Lab., Livermore, Calif., 1974.
	11	HULL, T.E., ENRIGHT, W.H., AND JACKSON, K.R. Users guide to DVERK--a subroutine for solving non-stiff ODE's. Rep. 100, Dep. of Comptr. Sel., U. of Toronto, Canada, 1976.
	12	NAG Manual, Mark 7. NAG Central Office, 7 Banbury Road, Oxford, England, 1979.
	13	PR~CE, J.D. Software for Sturm-Liouville elgenvalues with error bounds. Rep. BUCSTR 79-02, Comptr. Sci. Dep., U of Bristol, England, 1978. Submitted for pubhcation.
	14	SHAMPINE, L.F. Better software for O.D.E.'s. Rep. SAND 78-1352, Sancha Labs., Albuquerque, N. Mex., 1978.
	15	L. F. Shampine, Stiffness and Nonstiff Differential Equation Solvers, II: Detecting Stiffness with Runge-Kutta Methods, ACM Transactions on Mathematical Software (TOMS), v.3 n.1, p.44-53, March 1977 [doi>10.1145/355719.355722]
	16	SHAMPINE, L.F., AND HIEBERT, K L. Detecting stiffness with the Fehlberg (4, 5) formulas. Comput. Math. Appl. 3 (1977), 41-46.
	17	L. F. Shampine , H. A. Watts, Global Error Estimates for Ordinary Differential Equations, ACM Transactions on Mathematical Software (TOMS), v.2 n.2, p.172-186, June 1976 [doi>10.1145/355681.355687]
	18	SHAMPINE, L.F., AND WATTS, H.A. Practical solution of ordinary differential equations by Runge- Kutta methods. Rep. SAND 76-0585, Sandia Labs., Albuquerque, N. Mex., 1976
	19	SIEMIENIUCH, J.L. A study of a method of F.T. Krogh for the numerical solution of ordinary differentml equations. M.Sc. Th., U. of Manchester, England, 1972.

CITED BY 6

	R. W. Brankin , I. Gladwell , J. R. Dormand , P. J. Prince , W. L. Seward, Algorithm 670: a Runge-Kutta-Nyström code, ACM Transactions on Mathematical Software (TOMS), v.15 n.1, p.31-40, March 1989
	Michael Lucks , Ian Gladwell, Automated selection of mathematical software, ACM Transactions on Mathematical Software (TOMS), v.18 n.1, p.11-34, March 1992
	P. M. Dew , J. E. Walsh, A Set of Library Routines for Solving Parabolic Equations in One Space Variable, ACM Transactions on Mathematical Software (TOMS), v.7 n.3, p.295-314, Sept. 1981
	Gopal K. Gupta , Ron Sacks-Davis , Peter E. Tescher, A review of recent developments in solving ODEs, ACM Computing Surveys (CSUR), v.17 n.1, p.5-47, March 1985
	M. Berzins , R. W. Brankin , I. Gladwell, The stiff integrators in the NAG library, ACM SIGNUM Newsletter, v.23 n.2, p.16-23, April 1988
	I. Gladwell, The NAG library ordinary differential equations chapter and short term plans for its extension, ACM SIGNUM Newsletter, v.20 n.3, p.35-40, July 1985

INDEX TERMS

Primary Classification:
G. Mathematics of Computing

Additional Classification:
G. Mathematics of Computing
G.1 NUMERICAL ANALYSIS
G.1.7 Ordinary Differential Equations
Subjects: Initial value problems

General Terms:
Theory

Collaborative Colleagues:

Ian Gladwell: colleagues

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