References - Lehrstuhl Numerische Mathematik - TUM
References - Lehrstuhl Numerische Mathematik - TUM References - Lehrstuhl Numerische Mathematik - TUM
REFERENCES 350 Nichols, N. K. (1994). Differential–algebraic equations and control system design. In Pitman Res. Notes Math. Ser., Volume 303, pp. 208–224. Longman Sci. Tech. Norsett, S. P. and P. Thomsen (1986). Local error control in SDIRK–methods. BIT 26, 100–113. Oden, J. T. and J. A. C. Martins (1985). Models and computational methods for dynamic friction phenomena. Comput. Meth. Appl. Mech. Engng. 85, 527–634. O’Malley Jr., R. E. (1991). Singular Perturbation Methods for Ordinary Differential Equations, Volume 89 of Appl. Mathem. Sci. New York, NY: Springer–Verlag. Pantelides, C. C. (1988). The consistent initialization of differential–algebraic systems. SIAM J. Sci. Stat. Comp. 9, 213–231. Pereia, M. and J. Ambrosio (1994). Computer Aided Analysis of Rigid and Flexible Mechanical Systems. Dordrecht, The Netherlands: Kluwer Acad. Publ. Petzold, L. R. (1982). Differential/algebraic equations are not ODEs. SIAM J. Sci. Stat. Comp. 3, 367–384. Petzold, L. R. (1986). Order results for implicit Runge–Kutta methods applied to differen- tial/algebraic systems. SIAM J. Numer. Anal. 23, 837–852. Petzold, L. R. and F. A. Potra (1992). ODAE methods for the numerical solution of Euler– Lagrange equations. Appl. Num. Math. 10, 397–413. Piirilä, O.-P. and J. Tuomela (1993). Differential–algebraic systems and formal integrability. Technical Report A326, Inst. of Mathem., Helsinki Univ. of Techn., Helsinki, Finnland. Pommaret, J. (1978). Systems of Partial Differential Equations and Lie Pseudogroups. New York, NY: Gordon and Breach. Pommaret, J. (1988). Lie Pseudogroups and Mechanics. New York, NY: Gordon and Breach. Porsching, T. A. (1985). A network model for two–fluid, two–phase flow. Num. Meth. Partial Diff. Equ. 1, 295–313. Potra, F. A. (1993). Implementation of linear multistep methods for solving constrained equa- tions of motion. SIAM J. Numer. Anal. 30, 774–789. Potra, F. A. and W. C. Rheinboldt (1989). Differential–geometric techniques for solving differential–algebraic equations. In E. Haug and R. Deyo (Eds.), Real–Time Integration Methods for Mech. System Simulation, Volume F 69 of NATO ASI Series, pp. 155–191. New York, NY: Springer–Verlag. Potra, F. A. and W. C. Rheinboldt (1991). On the numerical solution of the Euler–Lagrange equations. Mech. Struct. and Mach. 19, 1–18. Powell, M. J. D. (1978). A fast algorithm for nonlinearly constrained optimization calculations. In G. A. Watson (Ed.), Numerical Analysis, Dundee 1977, Volume 630 of Lect. Notes in Math., pp. 144–157. Berlin, Germany: Springer–Verlag. Prothero, A. and A. Robinson (1974). On the stability and accuracy of one–step methods for solving stiff systems of ordinary differential equations. Math. of Comp. 28, 145–162. Quéré, M.-P. (1994). Une forme normale pour les daes linéaires. Technical Report RT 122, LMC–IMAG, Grenoble, France. Quillen, D. (1964). Formal properties of overdetermined systems of linear partial differential equations. Ph. D. thesis, Harvard Univ., Cambridge, MA.
REFERENCES 351 Rabier, P. J. (1989). Implicit differential equations near a singular point. J. Math. Anal. Appl. 144, 425–449. Rabier, P. J. (1999). The Hopf bifurcation theorem for quasilinear differential–algebraic equa- tions. Comp. Meth. Appl. Mech. Engrg. 170, 355–371. Rabier, P. J. and G. W. Reddien (1986). Characterization and computation of singular points with maximum rank deficiency. SIAM J. Numer. Anal. 23, 1040–1051. Rabier, P. J. and W. C. Rheinboldt (1990). On a computational method for the second funda- mental tensor and its application to bifurcation problems. Numer. Math. 57, 681–694. Rabier, P. J. and W. C. Rheinboldt (1991). A general existence and uniqueness theory for implicit differential–algebraic equations. Diff. and Integral Equations 4, 563–582. Rabier, P. J. and W. C. Rheinboldt (1994a). Finite difference methods for time–dependent, linear differential algebraic equations. Appl. Math. Letters 7, 29–34. Rabier, P. J. and W. C. Rheinboldt (1994b). A geometric treatment of implicit differential– algebraic equations. J. Diff. Equations 109, 110–146. Rabier, P. J. and W. C. Rheinboldt (1994c). On impasse points of quasilinear differential– algebraic equations. J. Math. Anal. Appl. 181, 429–454. Rabier, P. J. and W. C. Rheinboldt (1994d). On the computation of impasse points of quasilinear differential–algebraic equations. Math. of Comp. 62, 133–154. Rabier, P. J. and W. C. Rheinboldt (1995). On the numerical solution of the Euler–Lagrange equations. SIAM J. Numer. Anal. 32, 318–329. Rabier, P. J. and W. C. Rheinboldt (1996a). Classical and generalized solutions of time– dependent linear DAEs. Lin. Alg. Appl. 245, 259–293. Rabier, P. J. and W. C. Rheinboldt (1996b). Discontinuous solutions of semilinear differential– algebraic equations. Part I: Distribution solutions. Nonlin. Anal.: Theory, Meth., Applic. 27, 1241–1256. Rabier, P. J. and W. C. Rheinboldt (1996c). Discontinuous solutions of semilinear differential– algebraic equations. Part II: P–consistency. Nonlin. Anal.: Theory, Meth., Applic. 27, 1257– 1280. Rabier, P. J. and W. C. Rheinboldt (1996d). Time–dependent linear DAEs with discontinuous inputs. Lin. Alg. Appl. 247, 1–29. Rabier, P. J. and W. C. Rheinboldt (2000). Nonholonomic Motion of Rigid Mechanical Systems from a DAE Viewpoint. Philadelphia, PA: SIAM Publications. Rath, W. (1995). Canonical forms for linear descriptor systems with variable coefficients. Tech- nical Report SPC 95–16, Sci. Parall. Comp., Techn. Univ. Chemnitz–Zwickau, Chemnitz, Germany. Reich, S. (1989). Beitrag zur Theorie der Algebrodifferentialgleichungen. Ph. D. thesis, Fakult. Elektrotech., Univ. Dresden, Dresden, Germany. Reich, S. (1990a). On a geometric characterization of differential–algebraic equations. Math. Res. 59, 105–113. Reich, S. (1990b). On a geometric interpretation of differential–algebraic equations. Circ. Syst. Signal Process. 9, 367–382.
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REFERENCES 350<br />
Nichols, N. K. (1994). Differential–algebraic equations and control system design. In Pitman<br />
Res. Notes Math. Ser., Volume 303, pp. 208–224. Longman Sci. Tech.<br />
Norsett, S. P. and P. Thomsen (1986). Local error control in SDIRK–methods. BIT 26, 100–113.<br />
Oden, J. T. and J. A. C. Martins (1985). Models and computational methods for dynamic<br />
friction phenomena. Comput. Meth. Appl. Mech. Engng. 85, 527–634.<br />
O’Malley Jr., R. E. (1991). Singular Perturbation Methods for Ordinary Differential Equations,<br />
Volume 89 of Appl. Mathem. Sci. New York, NY: Springer–Verlag.<br />
Pantelides, C. C. (1988). The consistent initialization of differential–algebraic systems. SIAM<br />
J. Sci. Stat. Comp. 9, 213–231.<br />
Pereia, M. and J. Ambrosio (1994). Computer Aided Analysis of Rigid and Flexible Mechanical<br />
Systems. Dordrecht, The Netherlands: Kluwer Acad. Publ.<br />
Petzold, L. R. (1982). Differential/algebraic equations are not ODEs. SIAM J. Sci. Stat.<br />
Comp. 3, 367–384.<br />
Petzold, L. R. (1986). Order results for implicit Runge–Kutta methods applied to differen-<br />
tial/algebraic systems. SIAM J. Numer. Anal. 23, 837–852.<br />
Petzold, L. R. and F. A. Potra (1992). ODAE methods for the numerical solution of Euler–<br />
Lagrange equations. Appl. Num. Math. 10, 397–413.<br />
Piirilä, O.-P. and J. Tuomela (1993). Differential–algebraic systems and formal integrability.<br />
Technical Report A326, Inst. of Mathem., Helsinki Univ. of Techn., Helsinki, Finnland.<br />
Pommaret, J. (1978). Systems of Partial Differential Equations and Lie Pseudogroups. New<br />
York, NY: Gordon and Breach.<br />
Pommaret, J. (1988). Lie Pseudogroups and Mechanics. New York, NY: Gordon and Breach.<br />
Porsching, T. A. (1985). A network model for two–fluid, two–phase flow. Num. Meth. Partial<br />
Diff. Equ. 1, 295–313.<br />
Potra, F. A. (1993). Implementation of linear multistep methods for solving constrained equa-<br />
tions of motion. SIAM J. Numer. Anal. 30, 774–789.<br />
Potra, F. A. and W. C. Rheinboldt (1989). Differential–geometric techniques for solving<br />
differential–algebraic equations. In E. Haug and R. Deyo (Eds.), Real–Time Integration<br />
Methods for Mech. System Simulation, Volume F 69 of NATO ASI Series, pp. 155–191.<br />
New York, NY: Springer–Verlag.<br />
Potra, F. A. and W. C. Rheinboldt (1991). On the numerical solution of the Euler–Lagrange<br />
equations. Mech. Struct. and Mach. 19, 1–18.<br />
Powell, M. J. D. (1978). A fast algorithm for nonlinearly constrained optimization calculations.<br />
In G. A. Watson (Ed.), Numerical Analysis, Dundee 1977, Volume 630 of Lect. Notes in<br />
Math., pp. 144–157. Berlin, Germany: Springer–Verlag.<br />
Prothero, A. and A. Robinson (1974). On the stability and accuracy of one–step methods for<br />
solving stiff systems of ordinary differential equations. Math. of Comp. 28, 145–162.<br />
Quéré, M.-P. (1994). Une forme normale pour les daes linéaires. Technical Report RT 122,<br />
LMC–IMAG, Grenoble, France.<br />
Quillen, D. (1964). Formal properties of overdetermined systems of linear partial differential<br />
equations. Ph. D. thesis, Harvard Univ., Cambridge, MA.
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