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Volumn 47, Issue 1, 2003, Pages 1-30

A high-order conservative Patankar-type discretisation for stiff systems of production-destruction equations

Author keywords

Conservativity; Patankar type schemes; Runge Kutta methods; Unconditional positivity

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL MODELS; STIFFNESS;

EID: 0041361873     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(03)00101-6     Document Type: Article
Times cited : (116)

References (36)
  • 2
    • 1942488739 scopus 로고
    • The European regional seas ecosystem model, a complex marine ecosystem model
    • Baretta J.W., Ebenhöh W., Ruardij P. The European regional seas ecosystem model, a complex marine ecosystem model. Neth. J. Sea Res. 33:1995;233-246.
    • (1995) Neth. J. Sea Res. , vol.33 , pp. 233-246
    • Baretta, J.W.1    Ebenhöh, W.2    Ruardij, P.3
  • 3
    • 0035443307 scopus 로고    scopus 로고
    • Modified mass matrices and positivity preservation for hyperbolic and parabolic PDEs
    • Berzins M. Modified mass matrices and positivity preservation for hyperbolic and parabolic PDEs. Commun. Numer. Meth. Engng. 9:2001;659-666.
    • (2001) Commun. Numer. Meth. Engng. , vol.9 , pp. 659-666
    • Berzins, M.1
  • 4
    • 0042567915 scopus 로고    scopus 로고
    • Applied Turbulence Modelling in Marine Waters
    • Berlin: Springer
    • Burchard H. Applied Turbulence Modelling in Marine Waters. Lecture Notes in Earth Sci. 100:2002;Springer, Berlin.
    • (2002) Lecture Notes in Earth Sci. , vol.100
    • Burchard, H.1
  • 5
    • 0001554040 scopus 로고
    • Positive cell-centered finite volume discretization methods for hyperbolic equations on irregular meshes
    • Berzins M., Ware J.M. Positive cell-centered finite volume discretization methods for hyperbolic equations on irregular meshes. Appl. Numer. Math. 16:1995;417-438.
    • (1995) Appl. Numer. Math. , vol.16 , pp. 417-438
    • Berzins, M.1    Ware, J.M.2
  • 6
    • 0343380277 scopus 로고    scopus 로고
    • Some mathematical problems associated with the development and use of marine models
    • J.I. Diaz. The Mathematics of Models for Climatology and Environment, Berlin: Springer
    • Deleersnijder E., Beckers J.-M., Campin J.-M., El Mohajir M., Fichefet T., Luyten P. Some mathematical problems associated with the development and use of marine models. Diaz J.I. The Mathematics of Models for Climatology and Environment. NATO ASI Ser. 48:1997;41-86 Springer, Berlin.
    • (1997) NATO ASI Ser. , vol.48 , pp. 41-86
    • Deleersnijder, E.1    Beckers, J.-M.2    Campin, J.-M.3    El Mohajir, M.4    Fichefet, T.5    Luyten, P.6
  • 8
    • 0027870061 scopus 로고
    • A Lagrangian model of phytoplankton growth dynamics for the Northern Adriatic Sea
    • Dippner J.W. A Lagrangian model of phytoplankton growth dynamics for the Northern Adriatic Sea. Cont. Shelf Res. 13:1993;331-355.
    • (1993) Cont. Shelf Res. , vol.13 , pp. 331-355
    • Dippner, J.W.1
  • 9
    • 0003239298 scopus 로고
    • Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations
    • Amsterdam: North-Holland
    • Dekker K., Verwer J.G. Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations. CWI Monogr. 2:1984;North-Holland, Amsterdam.
    • (1984) CWI Monogr. , vol.2
    • Dekker, K.1    Verwer, J.G.2
  • 10
    • 0028978369 scopus 로고
    • A model of the yearly cycle of nutrients and plankton in the Baltic Sea
    • Fennel W. A model of the yearly cycle of nutrients and plankton in the Baltic Sea. J. Mar. Sys. 6:1995;313-329.
    • (1995) J. Mar. Sys. , vol.6 , pp. 313-329
    • Fennel, W.1
  • 12
    • 0036679647 scopus 로고    scopus 로고
    • Operator splitting and approximate factorization for taxis-diffusion-reaction models
    • Gerisch A., Verwer J.G. Operator splitting and approximate factorization for taxis-diffusion-reaction models. Appl. Numer. Math. 42:(1-3):2002;159-176.
    • (2002) Appl. Numer. Math. , vol.42 , Issue.1-3 , pp. 159-176
    • Gerisch, A.1    Verwer, J.G.2
  • 16
    • 0043259448 scopus 로고
    • On a second order non-negativity conserving method
    • Horváth Z. On a second order non-negativity conserving method. Ann. Univ. Sci. Budapest Sect. Comput. 13:1992;237-242.
    • (1992) Ann. Univ. Sci. Budapest Sect. Comput. , vol.13 , pp. 237-242
    • Horváth, Z.1
  • 17
    • 38248999134 scopus 로고
    • Consistency and stability for some nonnegativity conserving methods
    • Horváth Z. Consistency and stability for some nonnegativity conserving methods. Appl. Numer. Math. 13:(5):1993;371-381.
    • (1993) Appl. Numer. Math. , vol.13 , Issue.5 , pp. 371-381
    • Horváth, Z.1
  • 18
    • 25544454987 scopus 로고
    • On higher order unconditionally nonnegative conserving methods
    • Horváth Z. On higher order unconditionally nonnegative conserving methods. Ann. Univ. Sci. Budapest Sect. Comput. 15:1995;167-178.
    • (1995) Ann. Univ. Sci. Budapest Sect. Comput. , vol.15 , pp. 167-178
    • Horváth, Z.1
  • 20
    • 0032183717 scopus 로고    scopus 로고
    • Positivity of Runge-Kutta and diagonally split Runge-Kutta methods
    • Horváth Z. Positivity of Runge-Kutta and diagonally split Runge-Kutta methods. Appl. Numer. Math. 28:1998;309-326.
    • (1998) Appl. Numer. Math. , vol.28 , pp. 309-326
    • Horváth, Z.1
  • 21
    • 38149146433 scopus 로고
    • Method of lines and direct discretization: A comparison for linear advection
    • Hundsdorfer W., Trompert R.A. Method of lines and direct discretization: A comparison for linear advection. Appl. Numer. Math. 13:(6):1994;469-490.
    • (1994) Appl. Numer. Math. , vol.13 , Issue.6 , pp. 469-490
    • Hundsdorfer, W.1    Trompert, R.A.2
  • 22
    • 0034580605 scopus 로고    scopus 로고
    • Partially implicit BDF2 blends for convection dominated flows
    • Hundsdorfer W. Partially implicit BDF2 blends for convection dominated flows. SIAM J. Numer. Anal. 38:(6):2001;1763-1783.
    • (2001) SIAM J. Numer. Anal. , vol.38 , Issue.6 , pp. 1763-1783
    • Hundsdorfer, W.1
  • 25
    • 0033841888 scopus 로고    scopus 로고
    • Towards a 3D-ecosystem model of the Baltic Sea
    • Neumann T. Towards a 3D-ecosystem model of the Baltic Sea. J. Mar. Sys. 25:2000;405-419.
    • (2000) J. Mar. Sys. , vol.25 , pp. 405-419
    • Neumann, T.1
  • 27
    • 0032028004 scopus 로고    scopus 로고
    • The use of TVD limiters for forward-in-time upstream-biased advection schemes in ocean modeling
    • Pietrzak J. The use of TVD limiters for forward-in-time upstream-biased advection schemes in ocean modeling. Monthly Weather Rev. 126:1998;812-830.
    • (1998) Monthly Weather Rev. , vol.126 , pp. 812-830
    • Pietrzak, J.1
  • 29
    • 0005354884 scopus 로고
    • The solution of a set of reaction rate equations
    • J. Walsh. New York: Academic Press
    • Robertson H.H. The solution of a set of reaction rate equations. Walsh J. Numerical Analysis, an Introduction. 1966;178-182 Academic Press, New York.
    • (1966) Numerical Analysis, an Introduction , pp. 178-182
    • Robertson, H.H.1
  • 31
    • 0043068657 scopus 로고    scopus 로고
    • Positive numerical integration methods for chemical kinetic systems
    • Sandu A. Positive numerical integration methods for chemical kinetic systems. J. Comput. Phys. 170:2001;589-602.
    • (2001) J. Comput. Phys. , vol.170 , pp. 589-602
    • Sandu, A.1
  • 32
    • 0041938834 scopus 로고    scopus 로고
    • Matrix Iterative Analysis
    • Berlin: Springer
    • Varga R.S. Matrix Iterative Analysis. Comput. Math. 27:2000;Springer, Berlin.
    • (2000) Comput. Math. , vol.27
    • Varga, R.S.1
  • 33
    • 0031275614 scopus 로고    scopus 로고
    • The iterative solution of fully implicit discretizations of three-dimensional transport models
    • van der Houwen P.J., Sommeijer B.P. The iterative solution of fully implicit discretizations of three-dimensional transport models. Appl. Numer. Math. 25:1997;243-256.
    • (1997) Appl. Numer. Math. , vol.25 , pp. 243-256
    • Van der Houwen, P.J.1    Sommeijer, B.P.2
  • 34
    • 0035281677 scopus 로고    scopus 로고
    • Approximate factorization for time-dependent partial differential equations
    • van der Houwen P.J., Sommeijer B.P. Approximate factorization for time-dependent partial differential equations. J. Comput. Appl. Math. 128:2001;447-466.
    • (2001) J. Comput. Appl. Math. , vol.128 , pp. 447-466
    • Van der Houwen, P.J.1    Sommeijer, B.P.2
  • 35
    • 0001637748 scopus 로고
    • Gauss-Seidel iteration for stiff ODEs from chemical kinetics
    • Verwer J.G. Gauss-Seidel iteration for stiff ODEs from chemical kinetics. SIAM J. Sci. Comput. 15:(5):1994;1243-1250.
    • (1994) SIAM J. Sci. Comput. , vol.15 , Issue.5 , pp. 1243-1250
    • Verwer, J.G.1
  • 36
    • 0028553604 scopus 로고
    • Simulating plankton ecosystems by the Lagrangian Ensemble method
    • Woods J.D., Barkmann W. Simulating plankton ecosystems by the Lagrangian Ensemble method. Philos. Trans. Roy. Soc. London B. 343:1994;27-31.
    • (1994) Philos. Trans. Roy. Soc. London B , vol.343 , pp. 27-31
    • Woods, J.D.1    Barkmann, W.2


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