[{"keyword":["Differential inclusions","implicit Euler method","numerical analysis"],"author":[{"id":"12477","last_name":"Beyn","full_name":"Beyn, Wolf-Jürgen","first_name":"Wolf-Jürgen"},{"full_name":"Rieger, Janosch","first_name":"Janosch","last_name":"Rieger"}],"abstract":[{"lang":"eng","text":"We propose a set-valued version of the implicit Euler scheme for relaxed one-sided Lipschitz differential inclusions and prove that the defining implicit inclusions have a well-defined solution. Furthermore, we give a convergence analysis based on stability theorems, which shows that the set-valued implicit Euler method inherits all favourable stability properties from the single-valued scheme. The impact of spatial discretization is discussed, a fully discretized version of the scheme is analyzed, and a numerical example is given."}],"date_updated":"2019-06-28T08:53:42Z","_id":"1795453","quality_controlled":"1","status":"public","title":"The implicit Euler scheme for one-sided Lipschitz differential inclusions","publisher":"American Institute of Mathematical Sciences","user_id":"67994","intvolume":" 14","doi":"10.3934/dcdsb.2010.14.409","publication_status":"published","external_id":{"isi":["000278676200007"]},"volume":14,"isi":1,"issue":"2","publication_identifier":{"issn":["1531-3492"]},"citation":{"apa":"Beyn, W. - J., & Rieger, J. (2010). The implicit Euler scheme for one-sided Lipschitz differential inclusions. *Discrete And Continuous Dynamical Systems. Series B*, *14*(2), 409-428. doi:10.3934/dcdsb.2010.14.409","bio1":"Beyn W-J, Rieger J (2010)

The implicit Euler scheme for one-sided Lipschitz differential inclusions.

Discrete And Continuous Dynamical Systems. Series B 14(2): 409-428.","apa_indent":"Beyn, W. - J., & Rieger, J. (2010). The implicit Euler scheme for one-sided Lipschitz differential inclusions. *Discrete And Continuous Dynamical Systems. Series B*, *14*(2), 409-428. doi:10.3934/dcdsb.2010.14.409

","chicago":"Beyn, Wolf-Jürgen, and Rieger, Janosch. 2010. “The implicit Euler scheme for one-sided Lipschitz differential inclusions”. *Discrete And Continuous Dynamical Systems. Series B* 14 (2): 409-428.

","default":"Beyn W-J, Rieger J (2010)

*Discrete And Continuous Dynamical Systems. Series B* 14(2): 409-428.","ama":"Beyn W-J, Rieger J. The implicit Euler scheme for one-sided Lipschitz differential inclusions. *Discrete And Continuous Dynamical Systems. Series B*. 2010;14(2):409-428.","mla":"Beyn, Wolf-Jürgen, and Rieger, Janosch. “The implicit Euler scheme for one-sided Lipschitz differential inclusions”. *Discrete And Continuous Dynamical Systems. Series B* 14.2 (2010): 409-428.","ieee":" W.-J. Beyn and J. Rieger, “The implicit Euler scheme for one-sided Lipschitz differential inclusions”, *Discrete And Continuous Dynamical Systems. Series B*, vol. 14, 2010, pp. 409-428.","wels":"Beyn, W. - J.; Rieger, J. (2010): The implicit Euler scheme for one-sided Lipschitz differential inclusions *Discrete And Continuous Dynamical Systems. Series B*,14:(2): 409-428.","frontiers":"Beyn, W. - J., and Rieger, J. (2010). The implicit Euler scheme for one-sided Lipschitz differential inclusions. *Discrete And Continuous Dynamical Systems. Series B* 14, 409-428.","lncs":" Beyn, W.-J., Rieger, J.: The implicit Euler scheme for one-sided Lipschitz differential inclusions. Discrete And Continuous Dynamical Systems. Series B. 14, 409-428 (2010).","dgps":"Beyn, W.-J. & Rieger, J. (2010). The implicit Euler scheme for one-sided Lipschitz differential inclusions. *Discrete And Continuous Dynamical Systems. Series B*, *14*(2), 409-428. American Institute of Mathematical Sciences. doi:10.3934/dcdsb.2010.14.409.

","harvard1":"Beyn, W.-J., & Rieger, J., 2010. The implicit Euler scheme for one-sided Lipschitz differential inclusions. *Discrete And Continuous Dynamical Systems. Series B*, 14(2), p 409-428.","angewandte-chemie":"W. - J. Beyn, and J. Rieger, “The implicit Euler scheme for one-sided Lipschitz differential inclusions”, *Discrete And Continuous Dynamical Systems. Series B*, **2010**, *14*, 409-428."},"article_type":"original","type":"journal_article","year":"2010","language":[{"iso":"eng"}],"publication":"Discrete And Continuous Dynamical Systems. Series B","department":[{"_id":"10020"},{"_id":"110284488"}],"page":"409-428","date_created":"2010-10-14T09:03:32Z"}]