DOI: 10.1007/bf02429858. Numerical integration of ordinary differential equations on manifolds

Numerical integration of ordinary differential equations on manifolds

10.1007/bf02429858

Crossref journal-article

Springer Science and Business Media LLC

Journal of Nonlinear Science (297)

Bibliography

Crouch, P. E., & Grossman, R. (1993). Numerical integration of ordinary differential equations on manifolds. Journal of Nonlinear Science, 3(1), 1â33.

Authors 2

P. E. Crouch (first)
R. Grossman (additional)

References 30 Referenced 255

M. Austin, P. S. Krishnaprasad, and L.-S. Wang, Symplectic and Almost Poisson Integration of Rigid Body Systems,Proceedings of the 1991 International Conference on Computational Engineering Science, ed. S. Atluvi, Melbourne, Australia, August, (1991).
J. C. Butcher, An Order Bound for Runge-Kutta Methods,SIAM J. Numerical Analysis, Vol. 12, pp. 304–315, (1975). (10.1137/0712025) / SIAM J. Numerical Analysis by J. C. Butcher (1975)
J. C. Butcher,The Numerical Analysis of Ordinary Differential Equations, John Wiley, (1986).
P. Channell, Symplectic Integration for Particles in Electric and Magnetic Fields, (Accelerator Theory Note, No. AT-6: ATN-86-5). Los Alamos National Laboratory, (1986).
P. Channell, and C. Scovel, Symplectic Integration of Hamiltonian Systems, submitted toNonlinearity, June, 1988.
A. Chorin, T. J. R. Hughes, J. E. Marsden, and M. McCracken, Product Formulas and Numerical Algorithms,Comm. Pure and Appl. Math., Vol. 31, pp. 205–256, (1978). (10.1002/cpa.3160310205) / Comm. Pure and Appl. Math. by A. Chorin (1978)
P. E. Crouch, Spacecraft Altitude Control and Stabilization: Application of Geometric Control to Rigid Body Models,IEEE Transactions on Automatic Control, Vol. AC-29, pp. 321–331, (1986). / IEEE Transactions on Automatic Control by P. E. Crouch (1986)
P. E. Crouch, and R. L. Grossman, The Explicit Computation of Integration Algorithms and First Integrals for Ordinary Differential Equations with Polynomial Coefficients Using Trees,Proceedings of the 1992 International Symposium of Algebraic and Symbolic Computation, ACM, (1992). (10.1145/143242.143277)
P. Crouch, R. Grossman, and R. G. Larson, Computations Involving Differential Operators and Their Actions on Functions,Proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation, ACM, (1991). (10.1145/120694.120740)
P. Crouch, R. Grossman, and R. Larson, Trees, Bialgebras, and Intrinsic Numerical Integrators, (Laboratory for Advanced Computing Technical Report, # LAC90-R23). University of Illinois at Chicago, May, (1990).
R. de Vogelaere, Methods of Integration which Preserve the Contact Transformation Property of the Hamiltonian Equations, Department of Mathematics, University of Notre Dame Report Vol. 4.
A. Deprit, Canonical Transformations Depending upon a Small Parameter,Celestial Mechanics, Vol. 1, pp. 1–31, (1969). / Celestial Mechanics by A. Deprit (1969)
A. J. Dragt, and J. M. Finn, Lie Series and Invariant Functions for Analytic Symplectic Maps,J. Math. Physics, Vol. 17, pp. 2215–2227, (1976). (10.1063/1.522868) / J. Math. Physics by A. J. Dragt (1976)
K. Feng, The Symplectic Methods for Computation of Hamiltonian Systems,Springer Lecture Notes in Numerical Methods for P.D.E.'s, (1987). (10.1007/BFb0078537)
C. W. Gear, Simultaneous numerical solution of differential-algebraic equations,IEEE Transactions on Circuit Theory, Vol. 18, pp. 89–95, (1971). (10.1109/TCT.1971.1083221) / IEEE Transactions on Circuit Theory by C. W. Gear (1971)
Ge-Zhong, and J. Marsden, Lie-Poisson Hamiltonian-Jacobi Theory and Lie-Poisson Integrations,Phys. Lett. A., Vol. 133, pp. 134–139, (1988). (10.1016/0375-9601(88)90773-6) / Phys. Lett. A. by Ge-Zhong (1988)
R. Grossman, and R. Larson, The Symbolic Computation of Derivations Using Labeled Trees,J. Sympolic Computation, to appear.
E. Hairer, C. Lubich, and M. Roche,The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods, Springer-Verlag, Berlin, (1989). (10.1007/BFb0093947) / The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods by E. Hairer (1989)
E. Hairer, S. P. Norsett, and G. Wanner,Solving Ordinary Differential Equations I: Nonstiff Problems, Springer-Verlag, Berlin, (1987). (10.1007/978-3-662-12607-3) / Solving Ordinary Differential Equations I: Nonstiff Problems by E. Hairer (1987)
E. Isaacson, and H. B. Keller,Analysis of Numerical Methods, Wiley, (1966).
A. J. Krener and R. Hermann, “Nonlinear Observability and Controllability,” IEEETransactions on Automatic Control A.C.-22, pp. 728–740, (1977). (10.1109/TAC.1977.1101601)
G. Meyer, On the Use of Euler's Theorem on Rotations for the Synthesis of Attitude Control Systems, (NASA Technical Note, NASA TN.D-3643). Ames Research Center, Moffet Field, California, (1966). / On the Use of Euler's Theorem on Rotations for the Synthesis of Attitude Control Systems / NASA Technical Note by G. Meyer (1966)
L. R. Petzold, Order Results for Implicit Runge-Kutta Methods Applied to Differential/Algebraic Systems,SIAM Journal of Numerical Analysis, Vol. 23, pp. 837–852, (1986). (10.1137/0723054) / SIAM Journal of Numerical Analysis by L. R. Petzold (1986)
W. C. Rheinboldt, Differential-Algebraic Systems as Differential Equations on Manifolds,Mathematics of Computation, Vol. 43, pp. 473–482, (1984). (10.1090/S0025-5718-1984-0758195-5) / Mathematics of Computation by W. C. Rheinboldt (1984)
R. Ruth, A Canonical Integration Technique,IEEE Transactions on Nuclear Science, Vol. 30, p. 2669, (1983). (10.1109/TNS.1983.4332919) / IEEE Transactions on Nuclear Science by R. Ruth (1983)
J. M. Sanz-Serra, Runge-Kutta Schemes for Hamiltonian Systems,Bit, Vol. 28, pp. 877–883, (1988). (10.1007/BF01954907) / Bit by J. M. Sanz-Serra (1988)
C. Scovel, Symplectic Numerical Integration of Hamiltonian Systems,Proceedings of the MSRI Workshop on the Geometry of Hamiltonian Systems, to appear. (10.1007/978-1-4613-9725-0_17)
F. Silva Leite, and J. Vitoria, Generalization of the De Moivre Formulas for Quaternions and Octonions,Estudos de Matematica in the Honour of Luis de Albequerque, Universidade de Coimbra, pp. 121–133, (1991).
F. Silva Leite, C. Simoes, and J. Vitoria, Hypercomplex Numbers and Rotations, Universidade Do Minho, 4–8, Vol. 3, pp. 636–643, (1987). / Universidade Do Minho by F. Silva Leite (1987)
Dao-Liu Wang, “Symplectic Difference Schemes for Hamiltonian Systems on Poisson Manifolds,” Academia Senica, Computing Center, Beijing, China, (1988). / Symplectic Difference Schemes for Hamiltonian Systems on Poisson Manifolds by Dao-Liu Wang (1988)

Dates

Type	When
Created	19 years ago (July 27, 2006, 5:05 a.m.)
Deposited	6 years, 3 months ago (May 17, 2019, 1:29 p.m.)
Indexed	3 weeks, 2 days ago (July 30, 2025, 11:24 a.m.)
Issued	31 years, 8 months ago (Dec. 1, 1993)
Published	31 years, 8 months ago (Dec. 1, 1993)
Published Print	31 years, 8 months ago (Dec. 1, 1993)

Funders 0

None

BibTeX

@article{Crouch_1993, title={Numerical integration of ordinary differential equations on manifolds}, volume={3}, ISSN={1432-1467}, url={http://dx.doi.org/10.1007/bf02429858}, DOI={10.1007/bf02429858}, number={1}, journal={Journal of Nonlinear Science}, publisher={Springer Science and Business Media LLC}, author={Crouch, P. E. and Grossman, R.}, year={1993}, month=dec, pages={1–33} }

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