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Volumn 38, Issue 4, 2001, Pages 1369-1388

Inexact simplified Newton iterations for implicit Runge-Kutta methods

Author keywords

Contraction; GMRES; Implicit Runge Kutta methods; Inexact simplified Newton methods; Linear iterative methods; Nonlinear equations; Ordinary differential equations; Preconditioning; Richardson iterations; Stiffness; W transformation

Indexed keywords


EID: 0034431557     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142999360573     Document Type: Article
Times cited : (39)

References (34)
  • 2
    • 0000144297 scopus 로고
    • Global approximate Newton methods
    • R. E. BANK AND D. J. ROSE, Global approximate Newton methods, Numer. Math., 37 (1981), pp. 279-295.
    • (1981) Numer. Math. , vol.37 , pp. 279-295
    • Bank, R.E.1    Rose, D.J.2
  • 3
    • 0022738825 scopus 로고
    • Matrix-free methods for stiff systems of ODE's
    • P. N. BROWN AND A. C. HINDMARSH, Matrix-free methods for stiff systems of ODE's, SIAM J. Numer. Anal., 23 (1986), pp. 610-638.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 610-638
    • Brown, P.N.1    Hindmarsh, A.C.2
  • 4
    • 0000286812 scopus 로고
    • Using Krylov methods in the solution of large-scale differential-algebraic systems
    • P. N. BROWN, A. C. HINDMARSH, AND L. R. PETZOLD, Using Krylov methods in the solution of large-scale differential-algebraic systems, SIAM J. Sci. Comput., 15 (1994), pp. 1467-1488.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 1467-1488
    • Brown, P.N.1    Hindmarsh, A.C.2    Petzold, L.R.3
  • 5
    • 0000977352 scopus 로고
    • Hybrid Krylov methods for nonlinear systems of equations
    • P. N. BROWN AND Y. SAAD, Hybrid Krylov methods for nonlinear systems of equations, SIAM J. Sci. Stat. Comput., 11 (1990), pp. 450-481.
    • (1990) SIAM J. Sci. Stat. Comput. , vol.11 , pp. 450-481
    • Brown, P.N.1    Saad, Y.2
  • 7
    • 0025557367 scopus 로고
    • On symmetric Runge-Kutta methods of high order
    • R. P. K. CHAN, On symmetric Runge-Kutta methods of high order, Computing, 45 (1990), pp. 301-309.
    • (1990) Computing , vol.45 , pp. 301-309
    • Chan, R.P.K.1
  • 8
    • 0001503361 scopus 로고
    • The use of iterative linear-equation solvers in codes for large systems of stiff IVPs for ODEs
    • T. F. CHAN AND K. R. JACKSON, The use of iterative linear-equation solvers in codes for large systems of stiff IVPs for ODEs, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 378-417.
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 378-417
    • Chan, T.F.1    Jackson, K.R.2
  • 9
    • 0012149379 scopus 로고
    • An iteration scheme for implicit Runge-Kutta methods
    • G. J. COOPER AND J. C. BUTCHER, An iteration scheme for implicit Runge-Kutta methods, IMA J. Numer. Anal., 3 (1983), pp. 127-140.
    • (1983) IMA J. Numer. Anal. , vol.3 , pp. 127-140
    • Cooper, G.J.1    Butcher, J.C.2
  • 10
    • 0025546535 scopus 로고
    • A scheme for the implementation of implicit Runge-Kutta methods
    • G. J. COOPER AND R. VIGNESVARAN, A scheme for the implementation of implicit Runge-Kutta methods, Computing, 45 (1990), pp. 321-332.
    • (1990) Computing , vol.45 , pp. 321-332
    • Cooper, G.J.1    Vignesvaran, R.2
  • 12
    • 0001330894 scopus 로고
    • Globally convergent inexact Newton method
    • S. C. EISENSTAT AND H. F. WALKER, Globally convergent inexact Newton method, SIAM J. Optim., 4 (1994), pp. 393-422.
    • (1994) SIAM J. Optim. , vol.4 , pp. 393-422
    • Eisenstat, S.C.1    Walker, H.F.2
  • 13
    • 0003176174 scopus 로고    scopus 로고
    • Choosing the forcing terms in an inexact Newton method
    • S. C. EISENSTAT AND H. F. WALKER, Choosing the forcing terms in an inexact Newton method, SIAM J. Sci. Comput., 17 (1996), pp. 16-32.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 16-32
    • Eisenstat, S.C.1    Walker, H.F.2
  • 14
    • 0008832102 scopus 로고    scopus 로고
    • A Set of GMRES Routines for Real and Complex Arithmetic
    • CERFACS, Toulouse, France
    • V. FRAYSSÉ, L. GIRAUD, AND S. GRATTON, A Set of GMRES Routines for Real and Complex Arithmetic, Tech. Rep. PA/97/49, CERFACS, Toulouse, France, 1997.
    • (1997) Tech. Rep. PA/97/49
    • Frayssé, V.1    Giraud, L.2    Gratton, S.3
  • 15
    • 0001436426 scopus 로고
    • Iterative solution of linear equations in ODE codes
    • G. W. GEAR AND Y. SAAD, Iterative solution of linear equations in ODE codes, SIAM J. Sci. Statist. Comput., 4 (1983), pp. 583-601.
    • (1983) SIAM J. Sci. Statist. Comput. , vol.4 , pp. 583-601
    • Gear, G.W.1    Saad, Y.2
  • 16
    • 0016072410 scopus 로고
    • On block elimination for sparse linear systems
    • A. GEORGE, On block elimination for sparse linear systems, SIAM J. Numer. Anal., 11 (1974), pp. 585-603.
    • (1974) SIAM J. Numer. Anal. , vol.11 , pp. 585-603
    • George, A.1
  • 19
    • 0000287695 scopus 로고
    • Iterative schemes for three-stage implicit Runge-Kutta methods
    • S. GONZÁLEZ-PINTO, J. I. MONTIJANO, AND L. RÁNDEZ, Iterative schemes for three-stage implicit Runge-Kutta methods, Appl. Numer. Math., 17 (1995), pp. 363-382.
    • (1995) Appl. Numer. Math. , vol.17 , pp. 363-382
    • González-Pinto, S.1    Montijano, J.I.2    Rández, L.3
  • 20
    • 0003241196 scopus 로고    scopus 로고
    • Iterative Methods for Solving Linear Systems
    • SIAM, Philadelphia
    • A. GREENBAUM, Iterative Methods for Solving Linear Systems, Frontiers Appl. Math. 17, SIAM, Philadelphia, 1997.
    • (1997) Frontiers Appl. Math. , vol.17
    • Greenbaum, A.1
  • 21
    • 0012912813 scopus 로고
    • Solving Ordinary Differential Equations I. Non-stiff problems
    • Springer-Verlag, Berlin
    • E. HAIRER, S. P. NØRSETT, AND G. WANNER, Solving Ordinary Differential Equations I. Non-stiff problems, 2nd ed., Springer Ser. Comput. Math. 18, Springer-Verlag, Berlin, 1993.
    • (1993) 2nd Ed., Springer Ser. Comput. Math. , vol.18
    • Hairer, E.1    Nørsett, S.P.2    Wanner, G.3
  • 22
    • 0038394260 scopus 로고
    • Algebraically stable and implementable Runge-Kutta methods of high order
    • E. HAIRER AND G. WANNER, Algebraically stable and implementable Runge-Kutta methods of high order, SIAM J. Numer. Anal., 18 (1981), pp. 1098-1108.
    • (1981) SIAM J. Numer. Anal. , vol.18 , pp. 1098-1108
    • Hairer, E.1    Wanner, G.2
  • 24
    • 0001449110 scopus 로고    scopus 로고
    • Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems
    • Springer-Verlag, Berlin
    • E. HAIRER AND G. WANNER, Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, 2nd ed., Springer Ser. Comput. Math. 14, Springer-Verlag, Berlin, 1996.
    • (1996) 2nd Ed., Springer Ser. Comput. Math. , vol.14
    • Hairer, E.1    Wanner, G.2
  • 25
    • 0038925108 scopus 로고    scopus 로고
    • Approximating Runge-Kutta matrices by triangular matrices
    • W. HOFFMANN AND J. J. B. DE SWART, Approximating Runge-Kutta matrices by triangular matrices, BIT, 37 (1997), pp. 346-354.
    • (1997) BIT , vol.37 , pp. 346-354
    • Hoffmann, W.1    De Swart, J.J.B.2
  • 26
    • 0000545837 scopus 로고    scopus 로고
    • Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems
    • L. JAY, Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems, SIAM J. Numer. Anal., 33 (1996), pp. 368-387.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 368-387
    • Jay, L.1
  • 27
    • 0032228613 scopus 로고    scopus 로고
    • Structure preservation for constrained dynamics with super partitioned additive Runge-Kutta methods
    • L. O. JAY, Structure preservation for constrained dynamics with super partitioned additive Runge-Kutta methods, SIAM J. Sci. Comput., 20 (1998), pp. 416-446.
    • (1998) SIAM J. Sci. Comput. , vol.20 , pp. 416-446
    • Jay, L.O.1
  • 28
    • 0347857867 scopus 로고    scopus 로고
    • Tech. Rep., Department of Math., University of Iowa, in preparation
    • L. O. JAY, User's Guide to SPARK3, Tech. Rep., Department of Math., University of Iowa, 2000, in preparation.
    • (2000) User's Guide to SPARK3
    • Jay, L.O.1
  • 29
    • 0033355808 scopus 로고    scopus 로고
    • A parallelizable preconditioner for the iterative solution of implicit Runge-Kutta type methods
    • L. O. JAY AND T. BRACONNIER, A parallelizable preconditioner for the iterative solution of implicit Runge-Kutta type methods, J. Comput. Appl. Math., 111 (1999), pp. 63-76.
    • (1999) J. Comput. Appl. Math. , vol.111 , pp. 63-76
    • Jay, L.O.1    Braconnier, T.2
  • 30
    • 0002914778 scopus 로고
    • Iterative Methods for Linear and Nonlinear Equations
    • SIAM, Philadelphia
    • C. T. KELLEY, Iterative Methods for Linear and Nonlinear Equations, Frontiers Appl. Math. 16, SIAM, Philadelphia, 1995.
    • (1995) Frontiers Appl. Math. , vol.16
    • Kelley, C.T.1
  • 33
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Y. SAAD AND M. H. SCHULTZ, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856-869.
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 34
    • 0030621829 scopus 로고    scopus 로고
    • Triangularly implicit iteration methods for ODE-IVP solvers
    • P. J. VAN DER HOUWEN AND J. J. B. DE SWART, Triangularly implicit iteration methods for ODE-IVP solvers, SIAM J. Sci. Comput., 18 (1997), pp. 41-55.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 41-55
    • Van Der Houwen, P.J.1    De Swart, J.J.B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.