References - Lehrstuhl Numerische Mathematik - TUM

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REFERENCES 340 Bader, G. and U. Ascher (1987). A new basis implementation for a mixed order boundary value ODE solver. SIAM J. Sci. Stat. Comp. 8, 483–500. Bauer, I., H. G. Bock, S. Körkel, and J. P. Schlöder (1999). Numerical methods for initial value problems and derivative generation for DAE models with application to optimum experimental design of chemical processes. In Proc. Int. Workshop on Scient. Comput. in Chem. Engin., Volume II. TU Hamburg Harburg, Germany. Bauer, I., H. G. Bock, D. B. Leineweber, and J. P. Schlöder (1999). Direct multiple shooting methods for control and optimization of DAEs in chemical engineering. In Proc. Int. Work- shop on Scient. Comput. in Chem. Engin., Volume II. TU Hamburg Harburg, Germany. Baumgarte, J. (1972). Stabilization of constraints and integrals of motion in dynamical systems. Comp. Meth. Appl. Mech. Eng. 1, 11–16. Beardmore, R. E. (1998). Stability and bifurcation properties of index–1 DAEs. Numer. Algo- rithms 19, 43–53. Becker, T. and V. Weispfenning (1993). Gröbner Bases, a Computational Approach to Commu- tative Algebra, Volume 141 of Grad. Texts in Mathem. New York, NY: Springer–Verlag. Berzins, M. and R. M. Furzeland (1985). A user’s manual for SPRINT – a versatile software package for solving systems of algebraic, ordinary, and partial differential equations. Tech- nical Report TNER.85.058, Thornton Res. Centre, Shell Research Ltd. Biegler, L. T. and J. J. Damiano (1986). Nonlinear parameter estimation: A case study. AIChE Journal 32, 29–45. Bishop, R. L. and R. J. Crittenden (1964). Geometry of Manifolds. New York, NY: Academic Press. Blajer, W. (1997). A geometric unification of constrained system dynamics. Multibody Syst. Dynam. 1, 3–21. Blajer, W. and A. Markiewicz (1995). The effect of friction on multibody dynamics. European J. Mech. Solids 14, 807–825. Bock, H. G., E. Eich, and J. P. Schlöder (1988). Numerical solution of constrained least squares boundary value problems in differential–algebraic equations. In K. Strehmel (Ed.), Numer- ical Treatment of Differential Equations. Leipzig, Germany: Teubner Verlag. Bock, H. G. and K. J. Plitt (1984). A multiple shooting algorithm for direct solution of constrained optimal control problems. In Proc. 9th IFAC World Congress, Budapest, Hungary, pp. 242–247. Pergamon Press. Bock, H. G., J. P. Schlöder, M. C. Steinbach, and H. Wörn (1997). Schnelle Roboter am Fliessband: Mathematische Bahnoptimierung in Praxis. In K. H. Hoffmann, W. Jäger, T. Lohmann, and H. Schunck (Eds.), <strong>Mathematik</strong> Schlüsseltechnologie für die Zukunft, pp. 539–550. Berlin, Germany: Springer–Verlag. Bornemann, F. A. (1998). Homogenization in Time of Singularly Perturbed Conservative Me- chanical Systems, Volume 1687 of Lect. Notes in Math. New York, NY: Springer–Verlag. Bremer, H. and P. Pfeiffer (1992). Elastische Mehrkörpersysteme. Stuttgart, Germany: Teubner Verlag. Brenan, K. E. (1983). Stability and convergence of difference approximations for higher index differential algebraic systems with applications in trajectory control. Ph. D. thesis, Univ. of Calif. at Los Angeles, Los Angeles, CA.
REFERENCES 341 Brenan, K. E., S. L. Campbell, and L. R. Petzold (1989). Numerical Solution of Initial–Value Problems in Differential–Algebraic Equations. New York, NY: Elsevier Science Publ. Brenan, K. E., S. L. Campbell, and L. R. Petzold (1996). Numerical Solution of Initial–Value Problems in Differential–Algebraic Equations, Volume 14 of Classics in Appl. Math. Philadel- phia, PA: SIAM Publications. Brenan, K. E. and B. E. Enquist (1988). Backward differentiation approximations of nonlinear differential/algebraic equations. Math. of Comp. 51, 659–676. Brenan, K. E. and L. R. Petzold (1989). The numerical solution of higher index differential/algebraic equations by implicit Runge–Kutta methods. SIAM J. Numer. Anal. 26, 976–996. Brown, P. N., A. C. Hindmarsh, and L. R. Petzold (1994). Using Krylov methods in the solution of large–scale differential algebraic systems. SIAM J. Sci. Stat. Comp. 15, 1467–1488. Burkardt, J. and W. C. Rheinboldt (1983). A locally parametrized continuation process. ACM Trans. Math. Softw. 9, 215–235. Burrage, K. and L. R. Petzold (1990). On order reduction for Runge–Kutta methods applied to differential/algebraic systems and to stiff systems of ODEs. SIAM J. Numer. Anal. 27, 447–456. Butcher, J. C. (1964). Implicit Runge–Kutta processes. Math. of Comp. 18, 50–64. Byrne, G. D. and A. C. Hindmarsh (1987). Stiff ODE solvers: A review of current and coming attractions. J. Comput. Phys. 70, 1–62. Cameron, I. T. (1983). Solution of differential–algebraic systems using diagonally–implicit Runge–Kutta methods. IMA J. Numer. Anal. 3, 273–289. Campbell, S. L. (1980). Singular Systems of Differential Equations, I. London, UK: Pitman Publ. Ltd. Campbell, S. L. (1982). Singular Systems of Differential Equations, II. London, UK: Pitman Publ. Ltd. Campbell, S. L. (1985). The numerical solution of higher index linear time varying singular systems of differential equations. SIAM J. Sci. Stat. Comp. 6, 334–348. Campbell, S. L. (1987). A general form for solvable linear time varying singular systems of differential equations. SIAM J. Math. Anal. 18, 1101–1115. Campbell, S. L. and C. W. Gear (1995). The index of general nonlinear DAEs. Numer. Math. 72, 173–196. Campbell, S. L. and E. Griepentrog (1995). Solvability of general differential algebraic equations. SIAM J. Sci. Stat. Comp. 16, 257–270. Campbell, S. L. and L. Petzold (1983). Canonical forms and solvable singular systems of differential equations. SIAM J. Alg. Disc. Meth. 4, 517–521. Caracotsios, M. and W. E. Stewart (1985). Sensitivity analysis of initial value problems with mixed ODEs and algebraic equations. Comp. and Chem. Eng. 9, 359–365. Cartan, E. (1945). Les Systèmes Différentiels Extérieurs et Leurs Applications Géométriques. Paris, France: Hermann. Cash, J. R. (1980). On the integration of stiff systems of ODEs using extended backward differentiation formulas. Numer. Math. 34, 235–246.
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