-
1
-
-
84983924133
-
Enclosure of Solutions of Ordinary Initial Value Problems and Applications
-
Adams, E., Ansorge, R., Großmann, Ch., and Roos, H. G. (eds), Akademie-Verlag, Berlin
-
Adams, E., Cordes, D., and Lohner, R.: Enclosure of Solutions of Ordinary Initial Value Problems and Applications, in: Adams, E., Ansorge, R., Großmann, Ch., and Roos, H. G. (eds), Discretization in Differential Equations and Enclosures, Akademie-Verlag, Berlin, 1987, pp. 9-28.
-
(1987)
Discretization in Differential Equations and Enclosures
, pp. 9-28
-
-
Adams, E.1
Cordes, D.2
Lohner, R.3
-
3
-
-
0005379467
-
-
Technical Report 1996-x5-94, Department of Mathematical Modelling, Technical University of Denmark, DK-2800, Lyngby, Denmark
-
Bendsten, C. and Stauning, O.: FADBAD, a Flexible C++ Package for Automatic Differentiation Using the Forward and Bachward Methods, Technical Report 1996-x5-94, Department of Mathematical Modelling, Technical University of Denmark, DK-2800, Lyngby, Denmark, 1996. FADBAD is available at http://www.imm.dtu.dk/fadbad.html.
-
(1996)
FADBAD, a Flexible C++ Package for Automatic Differentiation Using the Forward and Bachward Methods
-
-
Bendsten, C.1
Stauning, O.2
-
4
-
-
0005668167
-
-
Technical Report 1997-x5-94, Department of Mathematical Modelling, Technical University of Denmark, DK-2800, Lyngby, Denmark
-
Bendsten, C. and Stauning, O.: TADIFF, a Flexible C++ Package for Automatic Differentiation Using Taylor Series, Technical Report 1997-x5-94, Department of Mathematical Modelling, Technical University of Denmark, DK-2800, Lyngby, Denmark, 1997. TADIFF is available at http://www.imm.dtu.dk/fadbad.html.
-
(1997)
TADIFF, a Flexible C++ Package for Automatic Differentiation Using Taylor Series
-
-
Bendsten, C.1
Stauning, O.2
-
5
-
-
85162725910
-
Discretization Errors for Well-Set Cauchy Problems: I
-
Birkhoff, G. and Varga, R. S.: Discretization Errors for Well-Set Cauchy Problems: I, J. Math. and Phys. 44 (1965), pp. 1-23.
-
(1965)
J. Math. and Phys.
, vol.44
, pp. 1-23
-
-
Birkhoff, G.1
Varga, R.S.2
-
6
-
-
0001849172
-
Validating an a Priori Enclosure Using High-Order Taylor Series
-
Alefeld, G. and Frommer, A. (eds), Akademie Verlag, Berlin
-
Corliss, G. F. and Rihm, R.: Validating an A Priori Enclosure Using High-Order Taylor Series, in: Alefeld, G. and Frommer, A. (eds), Scientific Computing, Computer Arithmetic, and Validated Numerics, Akademie Verlag, Berlin, 1996, pp. 228-238.
-
(1996)
Scientific Computing, Computer Arithmetic, and Validated Numerics
, pp. 228-238
-
-
Corliss, G.F.1
Rihm, R.2
-
7
-
-
29244445741
-
Sur les dèveloppements en série des fonctions d'une seule variable
-
Darboux, G.: Sur les dèveloppements en série des fonctions d'une seule variable, J. des Mathématique pures et appl., 3ème série, t. II, 1876, pp. 291-312.
-
(1876)
J. des Mathématique Pures et Appl., 3ème Série
, vol.2
, pp. 291-312
-
-
Darboux, G.1
-
8
-
-
0039411239
-
On Padé Approximations to the Exponential Function and A-Stable Methods for the Numerical Solution of Initial Value Problems
-
Ehle, B. L.: On Padé Approximations to the Exponential Function and A-Stable Methods for the Numerical Solution of Initial Value Problems, SIAM J. Math. Anal. 4 (1973), pp. 671-680.
-
(1973)
SIAM J. Math. Anal.
, vol.4
, pp. 671-680
-
-
Ehle, B.L.1
-
10
-
-
0016443950
-
Comparing Numerical Methods for Stiff Systems of ODEs
-
Enright, W. H., Hull, T. E., and Lindberg, B.: Comparing Numerical Methods for Stiff Systems of ODEs, BIT 15 (1975), pp. 10-48.
-
(1975)
BIT
, vol.15
, pp. 10-48
-
-
Enright, W.H.1
Hull, T.E.2
Lindberg, B.3
-
11
-
-
0347643883
-
ODE Solving via Automatic Differentiation and Rational Prediction
-
Griffiths, D. F. and Watson, G. A. (eds), Numerical Analysis 1995, Addison-Wesley Longman Ltd
-
Griewank, A.: ODE Solving via Automatic Differentiation and Rational Prediction, in: Griffiths, D. F. and Watson, G. A. (eds), Numerical Analysis 1995, volume 344 of Pitman Research Notes in Mathematics Series, Addison-Wesley Longman Ltd, 1995.
-
(1995)
Pitman Research Notes in Mathematics Series
, vol.344
-
-
Griewank, A.1
-
12
-
-
0004798808
-
High-Order Stiff ODE Solvers via Automatic Differentiation and Rational Prediction
-
Springer, Berlin
-
Griewank, A., Corliss, G. F., Henneberger, P., Kirlinger, G., Potra, F. A., and Stetter, H. J.: High-Order Stiff ODE Solvers via Automatic Differentiation and Rational Prediction, in: Lecture Notes in Comput. Sci. 1196, Springer, Berlin, 1997, pp. 114-125.
-
(1997)
Lecture Notes in Comput. Sci.
, vol.1196
, pp. 114-125
-
-
Griewank, A.1
Corliss, G.F.2
Henneberger, P.3
Kirlinger, G.4
Potra, F.A.5
Stetter, H.J.6
-
13
-
-
0030168036
-
ADOL-C, a Package for the Automatic Differentiation of Algorithms Written in C/C++
-
Griewank, A., Juedes, D., and Utke, J.: ADOL-C, a Package for the Automatic Differentiation of Algorithms Written in C/C++, ACM Trans. Math. Software 22 (2) (1996), pp. 131-167.
-
(1996)
ACM Trans. Math. Software
, vol.22
, Issue.2
, pp. 131-167
-
-
Griewank, A.1
Juedes, D.2
Utke, J.3
-
14
-
-
0004317158
-
-
Springer-Verlag, 2nd revised edition
-
Hairer, E., Nørsett, S. P., and Wanner, G.: Solving Ordinary Differential Equations I. Nonstiff Problems, Springer-Verlag, 2nd revised edition, 1991.
-
(1991)
Solving Ordinary Differential Equations I. Nonstiff Problems
-
-
Hairer, E.1
Nørsett, S.P.2
Wanner, G.3
-
15
-
-
0242465561
-
Extrait d'une lettre de M. Ch. Hermite à M. Borchardt sur la formule d'interpolation de Lagrange
-
Oeuvres, tome III
-
Hermite, Ch.: Extrait d'une lettre de M. Ch. Hermite à M. Borchardt sur la formule d'interpolation de Lagrange, J. de Crelle 84 (70) (1878), Oeuvres, tome III, pp. 432-443.
-
(1878)
J. de Crelle
, vol.84
, Issue.70
, pp. 432-443
-
-
Hermite, Ch.1
-
16
-
-
0347013070
-
-
personal communications
-
Van Iwaarden, R.: IADOL-C, personal communications, 1997.
-
(1997)
IADOL-C
-
-
Van Iwaarden, R.1
-
17
-
-
0001292188
-
PROFIL/BIAS - A Fast Interval Library
-
Knüppel, O.: PROFIL/BIAS - a Fast Interval Library, Computing 53 (3-4) (1994), pp. 277-287. PROFIL/BIAS is available at http://www.ti3.tu-harburg.de/Software/PROFIL/Profil.texinfo_1.html.
-
(1994)
Computing
, vol.53
, Issue.3-4
, pp. 277-287
-
-
Knüppel, O.1
-
18
-
-
0005768986
-
Ordinary Differential Equations
-
Hansen, E. (ed.), Clarendon Press, Oxford
-
Krückeberg, F.: Ordinary Differential Equations, in: Hansen, E. (ed.), Topics in Interval Analysis, Clarendon Press, Oxford, 1969, pp. 91-97.
-
(1969)
Topics in Interval Analysis
, pp. 91-97
-
-
Krückeberg, F.1
-
21
-
-
0000466527
-
Enclosing the Solutions of Ordinary Initial and Boundary Value Problems
-
Kaucher, E. W., Kulisch, U. W., and Ullrich, Ch. (eds), Wiley-Teubner Series in Computer Science, Stuttgart
-
Lohner, R. J.: Enclosing the Solutions of Ordinary Initial and Boundary Value Problems, in: Kaucher, E. W., Kulisch, U. W., and Ullrich, Ch. (eds), Computer Arithmetic: Scientific Computation and Programming Languages, Wiley-Teubner Series in Computer Science, Stuttgart, 1987, pp. 255-286.
-
(1987)
Computer Arithmetic: Scientific Computation and Programming Languages
, pp. 255-286
-
-
Lohner, R.J.1
-
22
-
-
0041061754
-
Automatic Local Coordinate Transformations to Reduce the Growth of Error Bounds in Interval Computation of Solutions of Ordinary Differential Equations
-
Rail, L. B. (ed.), Wiley, New York
-
Moore, R. E.: Automatic Local Coordinate Transformations to Reduce the Growth of Error Bounds in Interval Computation of Solutions of Ordinary Differential Equations, in: Rail, L. B. (ed.), Error in Digital Computation, Vol. II, Wiley, New York, 1965, pp. 103-140.
-
(1965)
Error in Digital Computation
, vol.2
, pp. 103-140
-
-
Moore, R.E.1
-
23
-
-
0004293209
-
-
Prentice-Hall, Englewood Cliffs, N.J.
-
Moore, R. E.: Interval Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1966.
-
(1966)
Interval Analysis
-
-
Moore, R.E.1
-
24
-
-
0041061758
-
The Automatic Analysis and Control of Error in Digital Computation Based on the Use of Interval Numbers
-
Rail, L. B. (ed.), Wiley, New York
-
Moore, R. E.: The Automatic Analysis and Control of Error in Digital Computation Based on the Use of Interval Numbers, in: Rail, L. B. (ed.), Error in Digital Computation, Vol. I, Wiley, New York, 1965, pp. 61-130.
-
(1965)
Error in Digital Computation
, vol.1
, pp. 61-130
-
-
Moore, R.E.1
-
25
-
-
85044494237
-
Validated Solutions of Initial Value Problems for Ordinary Differential Equations
-
to appear
-
Nedialkov, N. S., Jackson, K. R., and Corliss, G. F.: Validated Solutions of Initial Value Problems for Ordinary Differential Equations, Applied Mathematics and Computation, to appear. Available at http://www.cs.toronto.edu/NA/reports.html.
-
Applied Mathematics and Computation
-
-
Nedialkov, N.S.1
Jackson, K.R.2
Corliss, G.F.3
-
26
-
-
0004134599
-
-
PhD thesis, Department of Computer Science, University of Toronto, Toronto, Canada, M5S 3G4
-
Nedialkov, N. S.: Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation, PhD thesis, Department of Computer Science, University of Toronto, Toronto, Canada, M5S 3G4. Aailable at http://www.cs.toronto.edu/NA/reports.html.
-
Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation
-
-
Nedialkov, N.S.1
-
30
-
-
0005675076
-
On a Class of Enclosure Methods for Initial Value Problems
-
Rihm, R.: On a Class of Enclosure Methods for Initial Value Problems, Computing 53 (1994), pp. 369-377.
-
(1994)
Computing
, vol.53
, pp. 369-377
-
-
Rihm, R.1
-
31
-
-
85013505430
-
NP-Hardness Results for Linear Algebraic Problems with Interval Data
-
Herzberger, J. (ed.), Topics in Validated Computations, North-Holland, Amsterdam
-
Rohn, J.: NP-Hardness Results for Linear Algebraic Problems with Interval Data, in: Herzberger, J. (ed.), Topics in Validated Computations, volume 5 of Studies in Computational Mathematics, North-Holland, Amsterdam, 1994, pp. 463-471.
-
(1994)
Studies in Computational Mathematics
, vol.5
, pp. 463-471
-
-
Rohn, J.1
-
32
-
-
0008656679
-
-
Technical Report IMM-PHD-1997-36, IMM, Lyngby, Denmark
-
Stauning, O.: Automatic Validation of Numerical Solutions, Technical Report IMM-PHD-1997-36, IMM, Lyngby, Denmark, 1997.
-
(1997)
Automatic Validation of Numerical Solutions
-
-
Stauning, O.1
-
33
-
-
85163206922
-
On Higher Order Stable Implicit Methods for Solving Parabolic Differential Equations
-
Varga, R. S.: On Higher Order Stable Implicit Methods for Solving Parabolic Differential Equations, J. Math. and Phys. 40 (1961), pp. 220-231.
-
(1961)
J. Math. and Phys.
, vol.40
, pp. 220-231
-
-
Varga, R.S.1
-
34
-
-
0005720846
-
-
Technical report, Université de Genéve, Section de Mathematique, 1211 Genéve 24th, Suisse
-
Wanner, G.: On the Integration of Stiff Differential Equations, Technical report, Université de Genéve, Section de Mathematique, 1211 Genéve 24th, Suisse, 1976.
-
(1976)
On the Integration of Stiff Differential Equations
-
-
Wanner, G.1
-
35
-
-
0005720846
-
On the Integration of Stiff Differential Equations
-
Proceedings of the Colloquium on Numerical Analysis Basel, Birkhäuser
-
Wanner, G.: On the Integration of Stiff Differential Equations, in: Proceedings of the Colloquium on Numerical Analysis, volume 37 of Internat. Ser. Numer. Math., Basel, Birkhäuser, 1977, pp. 209-226.
-
(1977)
Internat. Ser. Numer. Math.
, vol.37
, pp. 209-226
-
-
Wanner, G.1
|