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On a variational approach for the analysis and numerical simulation of ODEs
1. | Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain |
2. | E.T.S. Ingenieros Industriales, Universidad de Castilla La Mancha |
References:
[1] |
S. Amat and P. Pedregal, A variational approach to implicit ODEs and differential inclusions,, ESAIM-COCV, 15 (2009), 139.
|
[2] |
S. Amat, D. J. López and P. Pedregal, Numerical approximation to ODEs using a variational approach I: The basic framework,, to appear in Optimization., (). Google Scholar |
[3] |
W. Auzinger, R. Frank and G. Kirlinger, An extension of $B$-convergence for Runge-Kutta methods,, Appl. Num. Math., 9 (1992), 91.
|
[4] |
W. Auzinger, R. Frank and G. Kirlinger, Modern convergence theory for stiff initial value problems,, J. Comput. Appl. Math., 45 (1993), 5.
doi: 10.1016/0378-3782(93)90046-W. |
[5] |
G. D. Byrne and A. C. Hindmarsh, Stift ODE solvers: A review of current and coming attractions,, J. Comput. Phys., 70 (1987), 1.
|
[6] |
G. Dahlquist, A special stability problem for linear multistep methods,, BIT, 3 (1963), 27.
doi: 10.1007/BF01963532. |
[7] |
J. H. Ferziger and M. Peric, "Computational Methods for Fluid Dynamics,", Springer-Verlag, (1980).
|
[8] |
E. Hairer, C. Lubich and G. Wanner, "Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations,", Springer Series in Computational Mathematics, (2006).
|
[9] |
E. Hairer and G. Wanner, "Solving Ordinary Differential Equations II: Stiff and Differential Algebraic Problems,", Springer-Verlag, (1991).
|
[10] |
J. D. Lambert, "Numerical Methods for Ordinary Differntial Systems: The Initial Value Problem,", John Wiley and Sons Ltd. 1991., (1991).
|
[11] |
A. Lew, J. E. Marsden, M. Ortiz and M. West, Variational time integrators,, Internat. J. Numer. Methods Engrg., 60 (2004), 153.
|
[12] |
J. E. Marsden and M. West, Discrete mechanics and variational integrators,, Acta Numer., 10 (2001), 357.
|
[13] |
The MathWorks, Inc., MATLAB and SIMULINK,, Natick, (). Google Scholar |
[14] |
P. Pedregal, A variational approach to dynamical systems, and its numerical simulation,, Numer. Funct. Anal. Opt., 31 (2010), 1532.
doi: 10.1080/01630563.2010.497237. |
[15] |
J. Stoer and R. Bulirsch, "Introduction to Numerical Analysis,", Springer-Verlag. Second edition, (1993).
|
show all references
References:
[1] |
S. Amat and P. Pedregal, A variational approach to implicit ODEs and differential inclusions,, ESAIM-COCV, 15 (2009), 139.
|
[2] |
S. Amat, D. J. López and P. Pedregal, Numerical approximation to ODEs using a variational approach I: The basic framework,, to appear in Optimization., (). Google Scholar |
[3] |
W. Auzinger, R. Frank and G. Kirlinger, An extension of $B$-convergence for Runge-Kutta methods,, Appl. Num. Math., 9 (1992), 91.
|
[4] |
W. Auzinger, R. Frank and G. Kirlinger, Modern convergence theory for stiff initial value problems,, J. Comput. Appl. Math., 45 (1993), 5.
doi: 10.1016/0378-3782(93)90046-W. |
[5] |
G. D. Byrne and A. C. Hindmarsh, Stift ODE solvers: A review of current and coming attractions,, J. Comput. Phys., 70 (1987), 1.
|
[6] |
G. Dahlquist, A special stability problem for linear multistep methods,, BIT, 3 (1963), 27.
doi: 10.1007/BF01963532. |
[7] |
J. H. Ferziger and M. Peric, "Computational Methods for Fluid Dynamics,", Springer-Verlag, (1980).
|
[8] |
E. Hairer, C. Lubich and G. Wanner, "Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations,", Springer Series in Computational Mathematics, (2006).
|
[9] |
E. Hairer and G. Wanner, "Solving Ordinary Differential Equations II: Stiff and Differential Algebraic Problems,", Springer-Verlag, (1991).
|
[10] |
J. D. Lambert, "Numerical Methods for Ordinary Differntial Systems: The Initial Value Problem,", John Wiley and Sons Ltd. 1991., (1991).
|
[11] |
A. Lew, J. E. Marsden, M. Ortiz and M. West, Variational time integrators,, Internat. J. Numer. Methods Engrg., 60 (2004), 153.
|
[12] |
J. E. Marsden and M. West, Discrete mechanics and variational integrators,, Acta Numer., 10 (2001), 357.
|
[13] |
The MathWorks, Inc., MATLAB and SIMULINK,, Natick, (). Google Scholar |
[14] |
P. Pedregal, A variational approach to dynamical systems, and its numerical simulation,, Numer. Funct. Anal. Opt., 31 (2010), 1532.
doi: 10.1080/01630563.2010.497237. |
[15] |
J. Stoer and R. Bulirsch, "Introduction to Numerical Analysis,", Springer-Verlag. Second edition, (1993).
|
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