Abstract
A variety of theorems and properties of nonlinear DAEs were discussed in part I. This paper illustrates many of these ideas within the context of analyzing a specific nonlinear system that exhibits a variety of interesting features.
Similar content being viewed by others
References
K.E. Brenan, S.L. Campbell and L.R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations (SIAM, Philadelphia, PA, 1996).
S.L. Campbell, Linearization of DAEs along trajectories, Z. Angew. Math. Phys. 46 (1995) 70-84.
S.L. Campbell, R. Hollenbeck, K. Yeomans and Y. Zhong, Mixed symbolic-numerical computations with general DAEs I: system properties, Numer. Algorithms (1998), this volume.
S.L. Campbell and W. Marszalek, DAEs arising from traveling wave solutions of PDEs, J. Comput. Appl. Math. 82 (1997) 41-58.
W. Marszalek, Analysis of partial differential algebraic equations, Ph.D. thesis, North Carolina State University, Raleigh, NC (1997).
W. Marszalek and S.L. Campbell, DAEs arising from traveling wave solutions of PDEs II, Comput. Math. Appl., to appear.
W.C. Rheinboldt, MANPAK: A set of algorithms for computations on implicitly defined manifolds, Comput. Math. Appl. 32 (1996) 15-28.
W.C. Rheinboldt, Solving algebraically explicit DAEs with the MANPAK-manifold-algorithms, Comput. Math. Appl. 33 (1997) 31-43.
J. Smoller, Shock Waves and Reaction-Diffusion Equations (Springer, New York, 1983).
V. Venkatasubramanian, H. Schättler and J. Zaborszky, Local bifurcations and feasibility regions in differential-algebraic systems, IEEE Trans. Automat. Control 40 (1995) 1992-2013.
C.C. Wu, New theory of MHD shock waves, in: Viscous Profiles and Numerical Methods for Shock Waves, ed. M. Shearer (SIAM, Philadelphia, PA, 1991) pp. 209-236.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Campbell, S.L., Marszalek, W. Mixed symbolic–numerical computations with general DAEs II: An applications case study. Numerical Algorithms 19, 85–94 (1998). https://doi.org/10.1023/A:1019106507166
Issue Date:
DOI: https://doi.org/10.1023/A:1019106507166