메뉴 건너뛰기




Volumn 45, Issue 4, 2007, Pages 1600-1621

Error analysis of IMEX Runge-Kutta methods derived from differential-algebraic systems

Author keywords

Differential algebraic systems; Runge Kutta methods; Stiff problems

Indexed keywords

BOOLEAN ALGEBRA; ERRORS; MATRIX ALGEBRA; NUMERICAL ANALYSIS; RUNGE KUTTA METHODS; SETTLING TANKS;

EID: 49449088311     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/060656929     Document Type: Article
Times cited : (130)

References (20)
  • 1
    • 0031269714 scopus 로고    scopus 로고
    • Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
    • U. ASCHER. S. RUUTH, AND R. J. SPITERI, Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations, Appl. Numer. Math., 25 (1997), pp. 151-167.
    • (1997) Appl. Numer. Math , vol.25 , pp. 151-167
    • ASCHER, U.1    RUUTH, S.2    SPITERI, R.J.3
  • 2
    • 0001737039 scopus 로고
    • Implicit-explicit methods for time dependent PDE's
    • U. ASCHER, S. RUUTH. AND R. J. WETTON, Implicit-explicit methods for time dependent PDE's, Appl. Numer. Math., 32 (1995), pp. 797-823.
    • (1995) Appl. Numer. Math , vol.32 , pp. 797-823
    • ASCHER, U.1    RUUTH, S.2    WETTON, R.J.3
  • 3
    • 0030082938 scopus 로고    scopus 로고
    • An implicit-explicit approach for atmospheric transport-chemistry problems
    • J. G. BLOM, W. HUNDSDORFER, AND J. G. VERWER, An implicit-explicit approach for atmospheric transport-chemistry problems, Appl. Numer. Math., 20 (1996), pp. 191-209.
    • (1996) Appl. Numer. Math , vol.20 , pp. 191-209
    • BLOM, J.G.1    HUNDSDORFER, W.2    VERWER, J.G.3
  • 4
    • 49449114115 scopus 로고    scopus 로고
    • Ph.D. Thesis, Mathematics for the Technology, Department of Mathematics and Computer Science, University of Catania, Italy
    • S. BOSCARINO, On the Uniform Accuracy of Implicit-Explicit Runge-Kutta Methods, Ph.D. Thesis, Mathematics for the Technology, Department of Mathematics and Computer Science, University of Catania, Italy, 2005.
    • (2005) On the Uniform Accuracy of Implicit-Explicit Runge-Kutta Methods
    • BOSCARINO, S.1
  • 6
    • 0001407297 scopus 로고    scopus 로고
    • Uniformly accurate schemes for hyperbolic systems with relaxation
    • R. E. CAFLISCH, S. JIN. AND G. RUSSO, Uniformly accurate schemes for hyperbolic systems with relaxation, SIAM J. Numer. Anal., 34 (1997), pp. 246-281.
    • (1997) SIAM J. Numer. Anal , vol.34 , pp. 246-281
    • CAFLISCH, R.E.1    JIN, S.2    RUSSO, G.3
  • 7
    • 21844502665 scopus 로고
    • The index of general nonlinear DAEs
    • S. L. CAMPBELL AND C. W. GEAR, The index of general nonlinear DAEs, Numer. Math., 72 (1995), pp. 173-196.
    • (1995) Numer. Math , vol.72 , pp. 173-196
    • CAMPBELL, S.L.1    GEAR, C.W.2
  • 8
    • 0037216570 scopus 로고    scopus 로고
    • Additive Runge-Kutta schemes for convection-diffusion-reaction equations
    • M. H. CARPENTER AND C. A. KENNEDY, Additive Runge-Kutta schemes for convection-diffusion-reaction equations, Appl. Numer. Math., 44 (2003), pp. 139-181.
    • (2003) Appl. Numer. Math , vol.44 , pp. 139-181
    • CARPENTER, M.H.1    KENNEDY, C.A.2
  • 9
    • 84990689276 scopus 로고
    • Hyperbolic conservation laws with stiff relaxation terms and entropy
    • G. Q. CHEN, C. D. LEVERMORE, AND T.-P. LIU, Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math., 47 (1994), pp. 787-830.
    • (1994) Comm. Pure Appl. Math , vol.47 , pp. 787-830
    • CHEN, G.Q.1    LEVERMORE, C.D.2    LIU, T.-P.3
  • 10
    • 0031275886 scopus 로고    scopus 로고
    • On the stability of implicit-explicit linear multistep methods
    • J. FRANK, W. HUNDSDORFER, AND J. G. VERWER, On the stability of implicit-explicit linear multistep methods, Appl. Numer. Math., 25 (1997), pp. 193-205.
    • (1997) Appl. Numer. Math , vol.25 , pp. 193-205
    • FRANK, J.1    HUNDSDORFER, W.2    VERWER, J.G.3
  • 11
    • 0000694148 scopus 로고
    • Differential algebraic equations, indices, and integral algebraic equation
    • C. W. GEAR, Differential algebraic equations, indices, and integral algebraic equation, SIAM J. Numer. Anal., 27 (1990), pp. 1527-1534.
    • (1990) SIAM J. Numer. Anal , vol.27 , pp. 1527-1534
    • GEAR, C.W.1
  • 12
    • 0001599522 scopus 로고
    • Error of Runge Kutta methods for stiff problems via differential algebraic equations
    • E. HAIRER. C.H. LUBICH, AND M. ROCHE, Error of Runge Kutta methods for stiff problems via differential algebraic equations, BIT, 28 (1988), pp. 678-700.
    • (1988) BIT , vol.28 , pp. 678-700
    • HAIRER, E.1    LUBICH, C.H.2    ROCHE, M.3
  • 13
    • 0002690510 scopus 로고
    • Solving Ordinary Differential Equation II
    • Stiff and Differential Algebraic Problems, 2nd ed, Springer-Verlag, New York
    • E. HAIRER AND G. WANNER, Solving Ordinary Differential Equation II: Stiff and Differential Algebraic Problems, 2nd ed., Springer Ser. Comput. Math. 14, Springer-Verlag, New York, 1991, 1996.
    • (1991) Springer Ser. Comput. Math , vol.14
    • HAIRER, E.1    WANNER, G.2
  • 14
    • 0037401566 scopus 로고    scopus 로고
    • Implicit-explicit time stepping with spatial discontinuous finite elements
    • W. HUNDSDORFER AND J. JAFFRÉ, Implicit-explicit time stepping with spatial discontinuous finite elements, Appl. Numer. Math., 45 (2003), pp. 231-254.
    • (2003) Appl. Numer. Math , vol.45 , pp. 231-254
    • HUNDSDORFER, W.1    JAFFRÉ, J.2
  • 15
    • 0034431558 scopus 로고    scopus 로고
    • Central schemes for balance laws of relaxation type
    • S. F. LIOTTA, V. ROMANO, AND G. RUSSO, Central schemes for balance laws of relaxation type, SIAM J. Numer. Anal., 38 (2000), pp. 1337-1356.
    • (2000) SIAM J. Numer. Anal , vol.38 , pp. 1337-1356
    • LIOTTA, S.F.1    ROMANO, V.2    RUSSO, G.3
  • 18
    • 34047219061 scopus 로고    scopus 로고
    • High order asymptotically strong-stability-preserving methods for hyperbolic systems with stiff relaxation
    • Springer-Verlag, Berlin
    • L PARESCHI AND G. RUSSO, High order asymptotically strong-stability-preserving methods for hyperbolic systems with stiff relaxation, in Hyperbolic Problems: Theory, Numerics, Applications, Springer-Verlag, Berlin, 2003, pp. 241-251.
    • (2003) Hyperbolic Problems: Theory, Numerics, Applications , pp. 241-251
    • PARESCHI, L.1    RUSSO, G.2
  • 19
    • 28844475047 scopus 로고    scopus 로고
    • Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxations
    • L. PARESCHI AND G. RUSSO, Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxations, J. Sci. Comput., 25 (2005), pp. 129-155.
    • (2005) J. Sci. Comput , vol.25 , pp. 129-155
    • PARESCHI, L.1    RUSSO, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.