@Article{FreitasSilv:2014:SyMeIn,
               author = "Freitas, Celso Bernardo N{\'o}brega and Silva, Paulo S{\'e}rgio 
                         Pereira da",
          affiliation = "{Instituto Nacional de Pesquisas Espaciais (INPE)} and 
                         {Universidade de S{\~a}o Paulo (USP)}",
                title = "A symbolic-numerical method for integration of DAEs based on 
                         geometric control theory",
              journal = "Journal of Control, Automation and Electrical Systems",
                 year = "2014",
               volume = "25",
               number = "4",
                pages = "400--412",
             keywords = "Initial value problems, Nonlinear systems, Approximation results, 
                         DAEs, Differential algebraic equations, Efficient numerical 
                         analysis, Geometric control, Geometric control theory, Integration 
                         method, Symbolic and numerical calculations, Differential 
                         equations.",
             abstract = "This work describes a symbolic-numerical integration method for a 
                         class of differential algebraic equations (DAEs) known as 
                         semi-explicit systems. Our method relies on geometric theory of 
                         decoupling for nonlinear systems combined with efficient numerical 
                         analysis techniques. It uses an algorithm that applies symbolic 
                         and numerical calculations to build an explicit vector field 
                         {\"A}, whose integral curves with compatible initial conditions 
                         are the same solutions of the original DAE. Here, compatible 
                         initial conditions are the ones that respect the algebraic 
                         restrictions and their derivatives up to their relative degree. 
                         This extended set of restrictions defines a submanifold of the 
                         whole space, which is formed by all the variables of the system, 
                         and all solutions of the DAE lie on this submanifold. Furthermore, 
                         even for nonexactly compatible initial conditions, the solutions 
                         of this explicit system defined by {\"A} converge exponentially 
                         to . Under mild assumptions, an approximation result shows that 
                         the precision of the method is essentially controlled by the 
                         distance of the initial condition from . A scheme to compute 
                         compatible initial conditions with the DAE is also provided. 
                         Finally, simulations with benchmarks and comparisons with other 
                         available methods show that this is a suitable alternative for 
                         these problems, specially for nonexactly compatible initial 
                         conditions or high-index problems. © 2014 Brazilian Society for 
                         Automatics - SBA.",
                  doi = "10.1007/s40313-014-0115-9",
                  url = "http://dx.doi.org/10.1007/s40313-014-0115-9",
                 issn = "2195-3880 and 2195-3899",
                label = "scopus 2014-11 FreitasDaSi:2014:SyMeIn",
             language = "en",
           targetfile = "Freitas_symbolic.pdf",
        urlaccessdate = "26 abr. 2024"
}