论文信息 - Consistent initial conditions for unstructured higher index DAES: a computational study

Consistent initial conditions for unstructured higher index DAES: a computational study

Differential algebraic equations (DAEs) are implicit systems of ordinary differential equations, F (x′, x, t) = 0, for which the Jacobian Fx′ is always singular. DAEs arise in many applications. Significant progress has been made in developing numerical methods for solving DAEs. Determination of consistent initial conditions remains a difficult problem especially for large higher index DAEs. This paper looks at one approach for computing consistent initial conditions for these systems. The focus is on initializing higher index DAE integrators but the observations are relevant to the general problem of initialization of DAE integrators.

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

[2] S. Campbell. High-Index Differential Algebraic Equations , 1995 .

[3] Stephen L. Campbell,et al. Solvability of General Differential Algebraic Equations , 1995, SIAM J. Sci. Comput..

[4] C. D. Meyer,et al. Generalized inverses of linear transformations , 1979 .

[5] Stephen L. Campbell,et al. Constraint preserving integrators for general nonlinear higher index DAEs , 1995 .

[6] C. Kelley. Iterative Methods for Linear and Nonlinear Equations , 1987 .

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

[8] C. W. Gear,et al. The index of general nonlinear DAEs , 1995 .

[9] John E. Dennis,et al. Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[10] C. W. Gear,et al. Approximation methods for the consistent initialization of differential-algebraic equations , 1988 .

[11] Linda R. Petzold,et al. Consistent Initial Condition Calculation for Differential-Algebraic Systems , 1998, SIAM J. Sci. Comput..

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