On the solution of differential-algebraic equations through gradient flow embedding

Author E. A. del Rio-Chanona would like to acknowledge CONACyT scholarship No. 522530 for funding this project.

[1]  S. Campbell,et al.  The additional dynamics of least squares completions for linear differential algebraic equations , 2007 .

[2]  C. W. Gear,et al.  Simultaneous Numerical Solution of Differential-Algebraic Equations , 1971 .

[3]  P. Powell Calculating Determinants of Block Matrices , 2011, 1112.4379.

[4]  Walter Murray,et al.  An efficient gradient flow method for unconstrained optimization , 1998 .

[5]  Ernst Hairer,et al.  The numerical solution of differential-algebraic systems by Runge-Kutta methods , 1989 .

[6]  C. Pantelides The consistent intialization of differential-algebraic systems , 1988 .

[7]  Wolfgang Marquardt,et al.  Computing consistent initial conditions for differential-algebraic equations , 1992 .

[8]  Stephen L. Campbell,et al.  Completions of nonlinear DAE flows based on index reduction techniques and their stabilization , 2009, J. Comput. Appl. Math..

[9]  Andreas A. Linninger,et al.  Symbolic numeric index analysis algorithm for differential algebraic equations , 2004 .

[10]  W. Marquardt,et al.  Structural analysis of differential-algebraic equation systems—theory and applications , 1995 .

[11]  R. Sargent,et al.  The mathematical modelling of transient systems using differential-algebraic equations , 1988 .

[12]  Uri M. Ascher,et al.  Stability of Computational Methods for Constrained Dynamics Systems , 1991, SIAM J. Sci. Comput..

[13]  Alexandre K. W. Navarro,et al.  Computer algebra systems coming of age: Dynamic simulation and optimization of DAE systems in Mathematica™ , 2014, Comput. Chem. Eng..

[14]  Wolfgang Marquardt,et al.  Getting around consistent initialization of DAE systems , 1997 .

[15]  M. Bartholomew-Biggs,et al.  Some effective methods for unconstrained optimization based on the solution of systems of ordinary differential equations , 1989 .

[16]  Uri M. Ascher,et al.  Computer methods for ordinary differential equations and differential-algebraic equations , 1998 .

[17]  Anders Barrlund,et al.  Constrained least squares methods for linear timevarying DAE systems , 1991 .

[18]  E. Hairer,et al.  Solving Ordinary Differential Equations II , 2010 .