[{"publisher":"ACADEMIC PRESS INC ELSEVIER SCIENCE","keyword":["center manifolds","numerical methods","bordered","linear systems","Hamiltonian systems"],"title":"The numerical approximation of center manifolds in Hamiltonian systems","doi":"10.1016/j.jmaa.2003.05.001","status":"public","user_id":"67994","year":"2003","date_created":"2010-04-28T12:58:36Z","abstract":[{"lang":"eng","text":"In this paper we develop a numerical method for computing higher order local approximations of center manifolds near steady states in Hamiltonian systems. The underlying system is assumed to be large in the sense that a large sparse Jacobian at the equilibrium occurs, for which only a linear solver and a low-dimensional invariant subspace is available. Our method combines this restriction from linear algebra with the requirement that the center manifold is parametrized by a symplectic mapping and that the reduced equation preserves the Hamiltonian form. Our approach can be considered as a special adaptation of a general method from Numer. Math. 80 (1998) 1-38 to the Hamiltonian case such that approximations of the reduced Hamiltonian are obtained simultaneously. As an application we treat a finite difference system for an elliptic problem on an infinite strip. (C) 2003 Elsevier Inc. All rights reserved."}],"language":[{"iso":"eng"}],"publication":"Journal of Mathematical Analysis and Applications","_id":"1609415","publication_identifier":{"issn":["0022-247X"]},"volume":288,"page":"28-46","author":[{"first_name":"WH","last_name":"Du","full_name":"Du, WH"},{"full_name":"Beyn, Wolf-Jürgen","last_name":"Beyn","id":"12477","first_name":"Wolf-Jürgen"}],"issue":"1","date_updated":"2019-07-04T15:31:11Z","publication_status":"published","intvolume":" 288","type":"journal_article","isi":1,"external_id":{"isi":["000187210100004"]},"article_type":"original","quality_controlled":"1","department":[{"_id":"10020"}],"citation":{"wels":"Du, W. H.; Beyn, W. - J. (2003): The numerical approximation of center manifolds in Hamiltonian systems Journal of Mathematical Analysis and Applications,288:(1): 28-46.","apa_indent":"
Du, W. H., & Beyn, W. - J. (2003). The numerical approximation of center manifolds in Hamiltonian systems. Journal of Mathematical Analysis and Applications, 288(1), 28-46. doi:10.1016/j.jmaa.2003.05.001
","frontiers":"Du, W. H., and Beyn, W. - J. (2003). The numerical approximation of center manifolds in Hamiltonian systems. Journal of Mathematical Analysis and Applications 288, 28-46.","harvard1":"Du, W.H., & Beyn, W.-J., 2003. The numerical approximation of center manifolds in Hamiltonian systems. Journal of Mathematical Analysis and Applications, 288(1), p 28-46.","ieee":" W.H. Du and W.-J. Beyn, “The numerical approximation of center manifolds in Hamiltonian systems”, Journal of Mathematical Analysis and Applications, vol. 288, 2003, pp. 28-46.","chicago":"
Du, WH, and Beyn, Wolf-Jürgen. 2003. “The numerical approximation of center manifolds in Hamiltonian systems”. Journal of Mathematical Analysis and Applications 288 (1): 28-46.
","dgps":"
Du, W.H. & Beyn, W.-J. (2003). The numerical approximation of center manifolds in Hamiltonian systems. Journal of Mathematical Analysis and Applications, 288(1), 28-46. ACADEMIC PRESS INC ELSEVIER SCIENCE. doi:10.1016/j.jmaa.2003.05.001.
","ama":"Du WH, Beyn W-J. The numerical approximation of center manifolds in Hamiltonian systems. Journal of Mathematical Analysis and Applications. 2003;288(1):28-46.","mla":"Du, WH, and Beyn, Wolf-Jürgen. “The numerical approximation of center manifolds in Hamiltonian systems”. Journal of Mathematical Analysis and Applications 288.1 (2003): 28-46.","lncs":" Du, W.H., Beyn, W.-J.: The numerical approximation of center manifolds in Hamiltonian systems. Journal of Mathematical Analysis and Applications. 288, 28-46 (2003).","apa":"Du, W. H., & Beyn, W. - J. (2003). The numerical approximation of center manifolds in Hamiltonian systems. Journal of Mathematical Analysis and Applications, 288(1), 28-46. doi:10.1016/j.jmaa.2003.05.001","angewandte-chemie":"W. H. Du, and W. - J. Beyn, “The numerical approximation of center manifolds in Hamiltonian systems”, Journal of Mathematical Analysis and Applications, 2003, 288, 28-46.","bio1":"Du WH, Beyn W-J (2003)
The numerical approximation of center manifolds in Hamiltonian systems.
Journal of Mathematical Analysis and Applications 288(1): 28-46.","default":"Du WH, Beyn W-J (2003)
Journal of Mathematical Analysis and Applications 288(1): 28-46."}}]