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Volumn 91, Issue 4, 2002, Pages 577-603

Runge-Kutta methods without order reduction for linear initial boundary value problems

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EID: 0036627738     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110100332     Document Type: Article
Times cited : (43)

References (32)
  • 1
    • 0000496713 scopus 로고    scopus 로고
    • On the removal of boundary errors caused by Runge-Kutta integration of nonlinear partial differential equations
    • S. Abarbanel, D. Gottlieb, M. H. Carpenter: On the removal of boundary errors caused by Runge-Kutta integration of nonlinear partial differential equations. SIAM J. Sci. Comput. 17, 777-782 (1996)
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 777-782
    • Abarbanel, S.1    Gottlieb, D.2    Carpenter, M.H.3
  • 2
    • 0033208033 scopus 로고    scopus 로고
    • Single step methods with optimal order of convergence for partial differential equations
    • I. Alonso-Mallo: Single step methods with optimal order of convergence for partial differential equations. Appl. Num. Math. 31, 117-131 (1999)
    • (1999) Appl. Num. Math. , vol.31 , pp. 117-131
    • Alonso-Mallo, I.1
  • 3
    • 0034512458 scopus 로고    scopus 로고
    • Rational methods with optimal order of convergence for partial differential equations
    • I. Alonso-Mallo: Rational methods with optimal order of convergence for partial differential equations. Appl. Num. Math. 35, 265-292 (2000)
    • (2000) Appl. Num. Math. , vol.35 , pp. 265-292
    • Alonso-Mallo, I.1
  • 5
    • 0042983532 scopus 로고    scopus 로고
    • On the convolutions operators arising in the study of abstract initial boundary value problems
    • I. Alonso-Mallo, C. Palencia: On the convolutions operators arising in the study of abstract initial boundary value problems. Proc. Royal Soc. Edinburgh. 126A, 515-539 (1996)
    • (1996) Proc. Royal Soc. Edinburgh. , vol.126 A , pp. 515-539
    • Alonso-Mallo, I.1    Palencia, C.2
  • 7
    • 0001308504 scopus 로고    scopus 로고
    • On implicit Runge-Kutta methods with high stage order
    • C. Bendtsen: On implicit Runge-Kutta methods with high stage order. BIT 37, 221-226 (1997)
    • (1997) BIT , vol.37 , pp. 221-226
    • Bendtsen, C.1
  • 8
    • 0001651846 scopus 로고
    • On rational approximations of semigroups
    • P. Brenner, V. Thomée: On rational approximations of semigroups. SIAM J. Numer. Anal. 16, 683-694 (1979)
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 683-694
    • Brenner, P.1    Thomée, V.2
  • 9
    • 0001899003 scopus 로고
    • Single step methods for non-homogeneous linear differential equations in Banach spaces
    • P. Brenner, M. Crouzeix, V. Thomée: Single step methods for non-homogeneous linear differential equations in Banach spaces. R.A.I.R.O. An. Num. 16, 5-26 (1982)
    • (1982) R.A.I.R.O. An. Num. , vol.16 , pp. 5-26
    • Brenner, P.1    Crouzeix, M.2    Thomée, V.3
  • 10
    • 8544220284 scopus 로고
    • Basic error estimates for elliptic problems
    • P. G. Ciarlet, J. L. Lions (eds.), Amsterdam: North-Holland
    • P.G. Ciarlet: Basic error Estimates for Elliptic Problems, Vol. II, Part 1, in Handbook of Numerical Analysis. P. G. Ciarlet, J. L. Lions (eds.), Amsterdam: North-Holland, 1991
    • (1991) Handbook of Numerical Analysis , vol.2 , Issue.PART 1
    • Ciarlet, P.G.1
  • 12
    • 70350334167 scopus 로고
    • Evolution problems
    • P. G. Ciarlet, J. L. Lions (eds.) Amsterdam: North-Holland
    • H. Fujita, T. Suzuki: Evolution Problems, Vol. II, Part 1, in Handbook of Numerical Analysis, P. G. Ciarlet, J. L. Lions (eds.) Amsterdam: North-Holland, 1991
    • (1991) Handbook of Numerical Analysis , vol.2 , Issue.PART 1
    • Fujita, H.1    Suzuki, T.2
  • 14
    • 84966262489 scopus 로고
    • Galerkin/Runge-Kutta discretizations for parabolic equations with time-dependent coefficients
    • S. Keeling: Galerkin/Runge-Kutta discretizations for parabolic equations with time-dependent coefficients. Math. Comput. 52, 561-586 (1989)
    • (1989) Math. Comput. , vol.52 , pp. 561-586
    • Keeling, S.1
  • 15
    • 0025413734 scopus 로고
    • Galerkin/Runge-Kutta discretizations for semilinear parabolic equations
    • S. Keeling: Galerkin/Runge-Kutta discretizations for semilinear parabolic equations. SIAM J. Numer. Anal. 27, 394-418 (1990)
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 394-418
    • Keeling, S.1
  • 16
    • 0000336284 scopus 로고
    • Explicit Runge-Kutta schemes for evolutionary problems in partial differential equations
    • T. Koto: Explicit Runge-Kutta schemes for evolutionary problems in partial differential equations. Annals of Numer. Math. 1, 335-346 (1994)
    • (1994) Annals of Numer. Math. , vol.1 , pp. 335-346
    • Koto, T.1
  • 17
    • 84968504982 scopus 로고
    • Runge-Kutta methods for parabolic equations and convolution quadrature
    • C. Lubich, A. Ostermann: Runge-Kutta methods for parabolic equations and convolution quadrature. Math. Comput. 60, 105-131 (1993)
    • (1993) Math. Comput. , vol.60 , pp. 105-131
    • Lubich, C.1    Ostermann, A.2
  • 18
    • 84968497603 scopus 로고
    • Runge-Kutta approximation of quasilinear parabolic equations
    • C. Lubich, A. Ostermann: Runge-Kutta approximation of quasilinear parabolic equations. Math. Comput. 64, 601-627 (1995)
    • (1995) Math. Comput. , vol.64 , pp. 601-627
    • Lubich, C.1    Ostermann, A.2
  • 19
    • 0000971789 scopus 로고
    • Interior estimates for time discretizations of parabolic equations
    • C. Lubich, A. Ostermann: Interior estimates for time discretizations of parabolic equations. App. Num. Math. 18, 241-251 (1995)
    • (1995) App. Num. Math. , vol.18 , pp. 241-251
    • Lubich, C.1    Ostermann, A.2
  • 21
    • 84968502295 scopus 로고
    • Runge-Kutta methods for partial differential equations and fractional orders of convergence
    • A. Ostermann, M. Roche: Runge-Kutta methods for partial differential equations and fractional orders of convergence. Math. Comput. 59, 403-420 (1992)
    • (1992) Math. Comput. , vol.59 , pp. 403-420
    • Ostermann, A.1    Roche, M.2
  • 22
    • 0027642259 scopus 로고
    • Rosenbrock methods for partial differential equations and fractional orders of convergence
    • A. Ostermann, M. Roche: Rosenbrock methods for partial differential equations and fractional orders of convergence. SIAM J. Numer. Anal. 30, 1084-1098 (1993)
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 1084-1098
    • Ostermann, A.1    Roche, M.2
  • 23
    • 0027681566 scopus 로고
    • A stability result for sectorial operators in Banach spaces
    • C. Palencia: A stability result for sectorial operators in Banach spaces. SIAM J. Numer. Anal. 30, 1373-1384 (1993)
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 1373-1384
    • Palencia, C.1
  • 24
    • 84968487151 scopus 로고
    • Stability of rational multistep approximations of holomorphic semigroups
    • C. Palencia: Stability of rational multistep approximations of holomorphic semigroups. Math. Comput. 64 (1995), 591-599
    • (1995) Math. Comput. , vol.64 , pp. 591-599
    • Palencia, C.1
  • 25
    • 0000957952 scopus 로고
    • Maximum norm analysis of completely discrete finite element methods for parabolic problems banach spaces
    • C. Palencia: Maximum norm analysis of completely discrete finite element methods for parabolic problems banach spaces. SIAM J. Numer. Anal. 33, 1654-1668 (1993)
    • (1993) SIAM J. Numer. Anal. , vol.33 , pp. 1654-1668
    • Palencia, C.1
  • 27
    • 0031215972 scopus 로고    scopus 로고
    • The correct formulation of intermediate boundary conditions for Runge-Kutta time integration of initial boundary value problems
    • D. Pathria: The correct formulation of intermediate boundary conditions for Runge-Kutta time integration of initial boundary value problems. SIAM J. Sci. Comput. 18, 1255-1266 (1997)
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 1255-1266
    • Pathria, D.1
  • 29
    • 38249024401 scopus 로고
    • Stability and convergence at the PDE/Stiff ODE interface
    • J.M. Sanz-Serna, J. G. Verwer: Stability and convergence at the PDE/Stiff ODE interface. Appl. Num. Math. 5, 117-132 (1989)
    • (1989) Appl. Num. Math. , vol.5 , pp. 117-132
    • Sanz-Serna, J.M.1    Verwer, J.G.2
  • 31
    • 0003208045 scopus 로고
    • Galerkin finite element methods for parabolic problems
    • Berlin: Springer
    • V. Thomée: Galerkin finite element methods for parabolic problems. In Lecture notes Math. Vol. 1054. Berlin: Springer, 1984
    • (1984) Lecture Notes Math. , vol.1054
    • Thomée, V.1
  • 32
    • 0013015362 scopus 로고
    • Finite element methods for evolution equations
    • W. Light (ed.). Oxford: Clarendon Press
    • L.B. Wahlbin: Finite element methods for evolution equations, in Advances in Numerical Analysis, Vol. 1, W. Light (ed.). Oxford: Clarendon Press, 1991
    • (1991) Advances in Numerical Analysis , vol.1
    • Wahlbin, L.B.1


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