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Papers

1997
978-1-4612-1960-6_12.pdf Petzold, L., Rosen, J. B., Gill, P. E., Jay, L. O., & Park K. (1997). Numerical Optimal Control of Parabolic PDEs using DASOPT. In: Biegler L.T., Coleman T.F., Conn A.R., Santosa F.N. (eds) Large-Scale Optimization with Applications. The IMA Volumes in Mathematics and its Applications, vol 93. Springer, New York, NY.
Numerical_Solution1.pdf Petzold, L. R., Jay, L. & Yen, J. (1997). Numerical Solution of Highly Oscillatory Ordinary Differential Equations. Acta Numerica 6, pp. 437-484
SCE000753.pdf Petzold, L. R., Ren, Y. & Maly, T. (1997). Regularization of Higher-Index Differential-Algebraic Equations with Rank-Deficient Constraints. SIAM J. Sci. Comput., 18(3), 753-774.
JOR000971.pdf Knapp, D. M., Barocas, V. H., Moon, A. G., Yoo, K., Petzold, L. R. & Tranquillo, R. T. (1997). Rheology of Reconstituted Type I Collagen Gel in Confined Compression. J. Rheol., 41(5), 971-993.
1996
sdarticle.pdf Ashby, S. F., Lee, S. L., Petzold, L. R., Saylor, P. E. & Seidel E. (1996). Computing Space-time Curvature via Differential-Algebraic Equations. Applied Numerical Mathematics 20, 221-234.
MalyPetz96.pdf Maly, T. & Petzold, L. R. (1996). Numerical Methods and Software for Sensitivity Analysis of Differential Algebraic Equations. Applied Numerical Mathematics 20, 57-79.
1995
CIP921995.pdf Hindmarsh, A. C. & Petzold, L. R. (1995). Algorithms and Software for Ordinary Differential Equations and Differential-Algebraic Equations, Part II: Higher-Order Methods and Software Packages. Computers in Physics, 9(2), 148-155.
convergence_of_the_iterative_methods_for_coordinat.pdf Yen, J. & Petzold, L. R. (1995). Convergence of the Iterative Methods for Coordinate Splitting Formulation in Multibody Dynamics. Technical Report
DASPK.pdf Van Keken, P. E., Yuen, D. A. & Petzold, L. R. (1995). DASPK: A New High Order and Adaptive Time-Integration Technique with Applications to Mantle Convection with Strongly Temperature and Pressure-Dependent Rheology. Geophys. Astrophys. Fluid Dynamics 80, 57-74.
Highly_Oscillatory.pdf Jay, L. O. & Petzold, L. R. (1995). Highly Oscillatory Systems and Periodic Stability. Technical Report
numerical_solution_of_nonlinear.pdf Yen, J. & Petzold, L. R. (1995). Numerical Solution of Nonlinear Oscillatory Multibody Dynamic Systems. Proc. of 16th Numerical Analysis Conference, University of Dundee.
CPE781995.pdf Maier, R. S., Petzold, L. R. & Rath, W. (1995). Parallel Solution of Large-Scale Differential-Algebraic Systems. Concurrency: Practice and Experience, 7(8), 795-822.
delay95.pdf Ascher, U. & Petzold, L. (1995). The Numerical Solution of Delay-Differential-Algebraic Equations of Retarded and Neutral Type. SIAM J. on Numerical Analysis 32, 1635-1657
1994
ANM151994.pdf Moore, P. K. & Petzold, L. R. (1994). A Stepsize Control Strategy for Stiff Systems of Ordinary Differential Equations. Applied Numerical Mathematics 15, 449-463.
Yen, J. & Petzold, L. R. (1994). On the Numerical Solution of Constrained Multibody Dynamic Systems. Technical Report
1993
SCE000095.pdf Ascher, U. M. & Petzold, L. R. (1993). Stability of Computational Methods for Constrained Dynamics Systems. SIAM J. Sci. Comput., 14(1), 95-120.
Stabilization071993.pdf Ascher, U. M., Chin, H., Petzold, L. R. & Reich, S. (1993). Stabilization of Constrained Mechanical Systems with DAEs and Invariant Manifolds. Technical Report
Krylov051993.pdf Brown, P. N., Hindmarsh, A. C. & Petzold, L. R. (1993). Using Krylov Methods in the Solutions of Large-Scale Differential-Algebraic Systems. Technical Report
1992
PD601992.pdf Petzold, L. R. (1992). Numerical Solution of Differential-Algebraic Equations in Mechanical Systems Simulation. Physica D 60, 269-279.
ANM101992.pdf Petzold, L. R. & Potra, F. A. (1992). ODAE Methods for the Numerical Solution of Euler-Lagrange Equations. Applied Numerical Mathematics 10, 397-413.
JCAM431992.pdf Ascher, U. M. & Petzold, L. R. (1992). Projected Collocation for Higher-Order Higher-Index Differential-Algebraic Equations. Journal of Computational and Applied Mathematics 43, 243-259.
1991
SNA000205.pdf Leimkuhler, B., Petzold, L. R. & Gear, C. W. (1991). Approximation Methods for the Consistent Initialization of Differential-Algebraic Equations. SIAM J. Numer. Anal., 28(1), 205-226.
SNA001097.pdf Ascher, U. M. & Petzold, L. R. (1991). Projected Implicit Runge-Kutta Methods for Differential-Algebraic Equations. SIAM J. Numer. Anal., 28(4), 1097-1120.
1990
llnl091990.pdf Ascher, U. M. & Petzold, L. R. (1990). Numerical Methods for Boundary Value Problems in Differential-Algebraic Equations. Proceedings from the AIChE National Meeting. Chicago, IL.
SNA000447.pdf Burrage, K. & Petzold, L. R. (1990). On Order Reduction for Runge-Kutta Methods Applied to Differential/Algebraic Systems and to Stiff Systems of ODEs. SIAM J. Numer. Anal., 27(2), 447-456.
1989
llnl061989.pdf Petzold, L. (1989). Methods and Software for Differential-Algebraic Systems. Proceedings from the NATO Advanced Research Workshop in Real-Time Integration Methods for Mechanical System Simulation. Snowbird, UT
llnl071989.pdf Petzold, L. R. (1989). Numerical Methods for Differential-Algebraic Equations Current Status and Future Directions. Proceedings from the Conference on Computational Ordinary Differential Equations. London, England.
SCE000915.pdf Clark, K. D. & Petzold, L. R. (1989). Numerical Solutions of Boundary Value Problems in Differential-Algebraic Systems. SIAM J. Sci. Stat. Comput., 10(5), 915-936.
CMAME75.pdf Petzold, L. R. (1989). Recent Developments in the Numerical Solution of Differential/Algebraic Systems. Computer Methods in Applied Mechanics and Engineering 75, 77-89. [Also appeared in (1990) Lectures in Applied Mathematics, 25, 177-190.]
SNA000976.pdf Brenan, K. E. & Petzold, L. R. (1989). The Numerical Solution of Higher Index Differential/Algebraic Equations by Implicit Methods. SIAM J. Numer. Anal., 26(4), 976-996.
1988
llnl101988.pdf Petzold, L. R. (1988). An Adaptive Moving Grid Method for One-Dimensional Systems of Partial Differential Equations and its Numerical Solution. Proceedings from the Workshop on Adaptive Methods for Partial Differential Equations. Troy, NY
llnl1988.pdf Hindmarsh, A. C. & Petzold, L. R. (1988). Numerical Methods for Solving Ordinary Differential Equations and Differential/Algebraic Equations. Energy and Technology Review, LLNL, September 1988
1987
llnl021987.pdf Petzold, L. R. (1987). Adaptive Moving Grid Strategies for One-Dimensional Systems of Partial Differential Equations. Proceedings from the Sixth IMACS International Symposium on Computer Methods for Partial Differential Equations. Lehigh, PA
ANM31987.pdf Petzold, L. R. (1987). Observations on an Adaptive Moving Grid Method for One-Dimensional Systems of Partial Differential Equations. Applied Numerical Mathematics 3, 347-360.
1986
SAND868893.pdf Kee, R. J. & Petzold, L. R. (1986). A Differential/Algebraic Equations Formulation of the Method-of-Lines Solution of Partial Differential Equations. Sandia Report
MC46174.pdf Lötstedt, P. & Petzold, L. R. (1986). Numerical Solution of Nonlinear Differential Equations with Algebraic Constraints I: Convergence Results for Backward Differentiation Formulas. Mathematics of Computation, 46(174), 491-516.
SCE000720.pdf Petzold, L. R. & Lötstedt, P. (1986). Numerical Solution of Nonlinear Differential Equations with Algebraic Constraints II: Practical Implications. SIAM J. Sci. Stat. Comput., 7(3), 720-733.
SNA000837.pdf Petzold, L. R. (1986). Order Results for Implicit Runge-Kutta Methods Applied to Differential/Algebraic Systems. SIAM J. Numer. Anal., 23(4), 837-852.
1985
kee_petzold.pdf Kee, R. J., Petzold, L. R., Smooke, M. D., & Grcar, J. F. (1985). Implicit Methods in Combustion and Chemical Kinetics Modeling. Multiple Time Scales, 113-144
1984
j._guidance.pdf LaFarge, R. A. and Petzold, L. R. (1984). An Exponentially Fitted Adams Method of Numerical Integration. Journal of Guidance, Control, and Dynamics, 7(3), 380-383
ODE_Methods.pdf Gear, C. W. & Petzold, L. R. (1984). ODE Methods for the Solution of Differential/Algebraic Systems. SIAM J. Num. Anal., 21(4), 716-728.
1983
SCE000136.pdf Petzold, L. R. (1983). Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations. SIAM J. Sci. Stat. Comput., 4(1), 136-148.
0604051.pdf Campbell, S. L. & Petzold, L. R. (1983). Canonical Forms and Solvable Singular Systems of Differential Equations. SIAM J. Alg. Disc. Meth., (4)4, 517-521.
differential_algebraic_systems_and_matric_pencils.pdf Gear, C. W. & Petzold, L. R. (1983). Differential/Algebraic Systems and Matrix Pencils. In: Kågström B., Ruhe A. (eds) Matrix Pencils. Lecture Notes in Mathematics, vol 973. Springer, Berlin, Heidelberg
10.1007-bfb0112529.pdf Gear, C. W., & Petzold, L. R. (1983). Singular Implicit Ordinary Differential Equations and Constraints. In: Numerical Methods. Lecture Notes in Mathematics, 1005. Berlin, Heidelberg, Springer.
1982
DASSL.pdf Petzold, L, R. (1982). A Description of DASSL: A Differential/Algebraic System Solver. Proc. IMACS World Congress
DAEs_not_ODEs.pdf Petzold, L. R. (1982). Differential/Algebraic Equations are not ODEs. SIAM J. Sci. Stat. Comput., 3(3), 367-384.
efam.pdf LaFarge, R. A., & Petzold, L. (1982). EFAM (Exponentially Fitted Adams Methods): A Numerical Integrator for Artillery Shells. Proceedings from the AIAA 9th Atmospheric Flight Mechanics Conference. San Diego, CA.
1981
SNA000455.pdf Petzold, L. R. (1981). An Efficient Numerical Method for Highly Oscillatory Ordinary Differential Equations. SIAM J. Numer. Anal., 18(3), 455-479.
revisited.pdf Gear, C. W., Hsu, H. H., & Petzold, L. (1981). Differential-Algebraic Equations Revisited. Proceedings from the meeting on Numerical Methods for Solving Stiff Initial Value Problems. Oberwolfach, Germany.

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