Index and Characteristic Analysis of Linear PDAE Systems

Automatable analyses of the index and well-posedness of two general classes of linear PDAEs are presented for use in equation-based dynamic simulation packages. These analyses determine whether a problem possesses a unique solution trajectory, the potential effect of noise in the initial and boundary conditions on the calculated solution, and the index of the model equations. Measures of the degeneracy of the system, rather than a differentiation index, bound the order of derivatives of forcing functions that appear in the solution.

[1]  H. Kreiss,et al.  Initial-Boundary Value Problems and the Navier-Stokes Equations , 2004 .

[2]  J. Strikwerda.  Finite Difference Schemes and Partial Differential Equations , 1989 .

[3]  Vincent G. Grassi.  Dynamic simulation as a tool to integrate process design and process control , 1993 .

[4]  Alan Jeffrey,et al.  Quasilinear hyperbolic systems and waves , 1976 .

[5]  L. Mirsky,et al.  The Theory of Matrices , 1961, The Mathematical Gazette.

[6]  W. Lucht,et al.  Indexes and Special Discretization Methods for Linear partial Differential Algebraic Equations , 1999 .

[7]  P. Roe.  CHARACTERISTIC-BASED SCHEMES FOR THE EULER EQUATIONS , 1986 .

[8]  Volker Mehrmann,et al.  A New Class of Discretization Methods for the Solution of Linear Differential-Algebraic Equations with Variable Coefficients , 1996 .

[9]  Paolo Antognetti,et al.  Semiconductor Device Modeling with Spice , 1988 .

[10]  Wieslaw Marszalek,et al.  The Index of an Infinite Dimensional Implicit System , 1999 .

[11]  R. F. Sincovec,et al.  Analysis of descriptor systems using numerical algorithms , 1981 .

[12]  Kristian Debrabant,et al.  On quasi-linear PDAEs with convection: applications, indices, numerical solution , 2002 .

[13]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

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

[15]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.

[16]  Paul I. Barton,et al.  A Differentiation Index for Partial Differential-Algebraic Equations , 1999, SIAM J. Sci. Comput..

[17]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[18]  L. Petzold.  Differential/Algebraic Equations are not ODE's , 1982 .

[19]  Michael Günther,et al.  Index Concepts for Linear Mixed Systems of Differential-Algebraic and Hyperbolic-Type Equations , 2000, SIAM J. Sci. Comput..

[20]  C. W. Gear,et al.  Differential-algebraic equations index transformations , 1988 .

[21]  James Demmel,et al.  The generalized Schur decomposition of an arbitrary pencil A–λB—robust software with error bounds and applications. Part I: theory and algorithms , 1993, TOMS.

[22]  Edward J. Longwell.  Dynamic modeling for process control and operability , 1994 .