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Automatic Solution of Differential Equations Based on the User of Linear Multistep Methods
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Source ACM Transactions on Mathematical Software (TOMS) archive
Volume 5 ,  Issue 4  (December 1979) table of contents
Pages: 401 - 414  
Year of Publication: 1979
ISSN:0098-3500
Authors
Zahari Zlatev  Institute of Mathematics and Statistics, Royal Veterinary and Agricultural University, Thorvaldsensvej 40, DK-1871, Copenhagen V, Denmark
Per Grove Thomsen  Institute for Numerical Analysis, Technical University of Denmark, DK-2800, Lyngby, Denmark
Publisher
ACM  New York, NY, USA
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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.

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ENRIGHT, W.H., BEDET, R., FARKAS, I., AND HULL, T.E. Test results on initial value methods for non-stiff ordinary differential equations. Tech. Rep. 68, Dep. of Comptr. Sci., U. of Toronto, Toronto, Canada, 1974.
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GEAR, C.W., AND Tu, K.W. The effect of variable mesh size on the stability of multistep methods. SlAM J. Numer. Anal. 11 (1974), 1025-1043.
 
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GEAR, C.W., AND WATANABE, D.S. Stability and convergence of variable order multistep methods. SIAM J. Numer. Anal. 11 (1974), 1044-1058.
 
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HENR:CI, P. Discrete Varmble Methods in Ordinary D~fferential Equattons. Wiley, New York, 1962.
 
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HINDMARSH, A.C. GEAR: Ordinary differential equation solver. Rep. UCRL - 51186, Lawrence Livermore Lab., Livermore, Calif, 1971.
 
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HULL, T.E., ENRIGHT, W.H., FELLEN, B.M., AND SEDGWlCK, A.E. Comparing numerical methods for ordinary differential equations. SIAM J. Numer. Anal. 9 (1972), 603-637.
 
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KLOPFENSTmN, R.D., AND MILLMAN, R.S. Numerical stability of one evaluation predictorcorrector algorithm for numerical solution of ordinary differential equations. Math. Comput. 22 (1968), 557-564.
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KROGH, F.T. VODQ/SVDQ/DVDQ--Variable order integrators for the numerical solution of ordinary differential equations. Jet Propulsion Lab., Pasadena, Calif., 1969.
 
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LAMBERT, J.D. Computational methods in ordinary differential equations. Wiley, New York, 1973.
 
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PIOTROWSKI, P. Stability, consistency and convergence of variable K-step methods for numerical integration of large systems of ordinary differential equations. In Proc. Conference on the Numerical Solutton of Dtfferential Equations (J.L. Morris, Ed.), Springer, New York, 1969, pp. 221-227.
 
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RODABAUGH, D., AND THOMPSON, S. Adams type methods with increased ranges of stability. Comptr. Math. Appl. 4 (1978), 349-357.
 
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RODABAUGH, D, AND THOMPSON, S. Corrector methods with increased ranges of stability. Comptr. Math. Appl. 3 (1977), 197-201.
 
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SEDGWICK, A.E. An effective variable order variable step Adams Method. Tech. Rep. 53, Dep. of Comptr. Sci., U. of Toronto, Toronto, Canada, 1973.
 
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SHAMPINE, L.F. Limiting precision in differential equations solvers. II: Sources of trouble and starting a code. Math. Comput. 32 (1978), 1115-1122.
 
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SHAMPINE, L.F. Solwng ordinary differential equations for simulation. Math. Comptr. S~mulation 20 (1978), 204-207.
 
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SHAMPINE, L.F. Stiffness and non-stiff differential equations solvers, in Numertsche Behandlung yon Differenhal-glewhungen (L. Collatz, Ed.). Int. Ser. Numer. Math., Vol. 27, Birkhanser, Basel, Switzerland, 1975, pp. 287-301.
 
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SHAMPINE, L.F., AND GORDOS, M.K. Computer Solutton of Ordinary Differentzal Equations: The Initial Value Problem. Freeman, San Francisco, 1975.
 
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SHAMPINE, L F., WATTS, H.A., AND DAVENPORT, S.M. Solving nonstiff ordinary differential equations--The state of the art. SIAM Rev. 18 (1976), 376-411.
 
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SCHOEN, K. Fifth and sixth order PECE algorithms with improved stability properties. SIAM J. Numer. Anal. 8 (1971), 244-248.
 
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STETTER, H.J. Analysis of D~screttzat~on Methods in Ordinary Dtfferentlal Equations. Springer, Berlin, 1973.
 
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STETTER, H.J. Improved absolute stability of predictor-corrector schemes. Computing 3 (1968), 286-296.
 
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THOMSEN, P.G., AND ZLATEV, Z. Two-parameters families of predictor-corrector methods for the solution of ordinary differential equations. Rep. NI-77-08, Institute for Numerical Analysis, Technical U. of Denmark, Lyngby, Denmark, 1977; to appear in BIT.
 
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ZLATEV, Z. Stability properties of variable stepsize variable formula methods. Numer. Math. 31 (1978), 175-182.

Collaborative Colleagues:
Zahari Zlatev: colleagues
Per Grove Thomsen: colleagues