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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, ESAIMCOCV, 15 (2009), 139148. 
[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. 
[3] 
W. Auzinger, R. Frank and G. Kirlinger, An extension of $B$convergence for RungeKutta methods, Appl. Num. Math., 9, (1992), 91109. 
[4] 
W. Auzinger, R. Frank and G. Kirlinger, Modern convergence theory for stiff initial value problems, J. Comput. Appl. Math., 45 (1993), 516. doi: 10.1016/03783782(93)90046W. 
[5] 
G. D. Byrne and A. C. Hindmarsh, Stift ODE solvers: A review of current and coming attractions, J. Comput. Phys., 70 (1987), 162. 
[6] 
G. Dahlquist, A special stability problem for linear multistep methods, BIT, 3 (1963), 2743. doi: 10.1007/BF01963532. 
[7] 
J. H. Ferziger and M. Peric, "Computational Methods for Fluid Dynamics," SpringerVerlag, Berlin, Germany, 1980. 
[8] 
E. Hairer, C. Lubich and G. Wanner, "Geometric Numerical Integration: StructurePreserving Algorithms for Ordinary Differential Equations," Springer Series in Computational Mathematics, Springer, 2006. 
[9] 
E. Hairer and G. Wanner, "Solving Ordinary Differential Equations II: Stiff and Differential Algebraic Problems," SpringerVerlag, Berlin, Germany, 1991. 
[10] 
J. D. Lambert, "Numerical Methods for Ordinary Differntial Systems: The Initial Value Problem," John Wiley and Sons Ltd. 1991. 
[11] 
A. Lew, J. E. Marsden, M. Ortiz and M. West, Variational time integrators, Internat. J. Numer. Methods Engrg., 60 (2004), 153212. 
[12] 
J. E. Marsden and M. West, Discrete mechanics and variational integrators, Acta Numer., 10 (2001), 357514. 
[13]  
[14] 
P. Pedregal, A variational approach to dynamical systems, and its numerical simulation, Numer. Funct. Anal. Opt., 31 (2010), 15322467. doi: 10.1080/01630563.2010.497237. 
[15] 
J. Stoer and R. Bulirsch, "Introduction to Numerical Analysis," SpringerVerlag. Second edition, 1993. 
show all references
References:
[1] 
S. Amat and P. Pedregal, A variational approach to implicit ODEs and differential inclusions, ESAIMCOCV, 15 (2009), 139148. 
[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. 
[3] 
W. Auzinger, R. Frank and G. Kirlinger, An extension of $B$convergence for RungeKutta methods, Appl. Num. Math., 9, (1992), 91109. 
[4] 
W. Auzinger, R. Frank and G. Kirlinger, Modern convergence theory for stiff initial value problems, J. Comput. Appl. Math., 45 (1993), 516. doi: 10.1016/03783782(93)90046W. 
[5] 
G. D. Byrne and A. C. Hindmarsh, Stift ODE solvers: A review of current and coming attractions, J. Comput. Phys., 70 (1987), 162. 
[6] 
G. Dahlquist, A special stability problem for linear multistep methods, BIT, 3 (1963), 2743. doi: 10.1007/BF01963532. 
[7] 
J. H. Ferziger and M. Peric, "Computational Methods for Fluid Dynamics," SpringerVerlag, Berlin, Germany, 1980. 
[8] 
E. Hairer, C. Lubich and G. Wanner, "Geometric Numerical Integration: StructurePreserving Algorithms for Ordinary Differential Equations," Springer Series in Computational Mathematics, Springer, 2006. 
[9] 
E. Hairer and G. Wanner, "Solving Ordinary Differential Equations II: Stiff and Differential Algebraic Problems," SpringerVerlag, Berlin, Germany, 1991. 
[10] 
J. D. Lambert, "Numerical Methods for Ordinary Differntial Systems: The Initial Value Problem," John Wiley and Sons Ltd. 1991. 
[11] 
A. Lew, J. E. Marsden, M. Ortiz and M. West, Variational time integrators, Internat. J. Numer. Methods Engrg., 60 (2004), 153212. 
[12] 
J. E. Marsden and M. West, Discrete mechanics and variational integrators, Acta Numer., 10 (2001), 357514. 
[13]  
[14] 
P. Pedregal, A variational approach to dynamical systems, and its numerical simulation, Numer. Funct. Anal. Opt., 31 (2010), 15322467. doi: 10.1080/01630563.2010.497237. 
[15] 
J. Stoer and R. Bulirsch, "Introduction to Numerical Analysis," SpringerVerlag. Second edition, 1993. 
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