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A semi-implicit mid-point rule for stiff systems of ordinary differential equations. (English) Zbl 0522.65050

MSC:
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
Software:
NSPIV; Larkin; GEAR
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References:
[1] Bader, G.: Numerische Behandlung steifer Differentialgleichungen mit einer modifizierten Mittelpunktsregel. Technische Universität München, Institut für Mathematik: Diploma thesis, 1977
[2] Bulirsch, R., Stoer, J.: Numerical Treatment of Ordinary Differential Equations by Extrapolation Methods. Numer. Math.8, 1-13 (1966) · Zbl 0135.37901
[3] Dahlquist, G.: A Special Stability Problem for Linear Multistep Methods. BIT3, 27-43 (1963) · Zbl 0123.11703
[4] Dahlquist, G., Lindberg, B.: On Some Implicit One-Step Methods for Stiff Differential Equations. Royal Institute of Technology, Stockholm: Tech. Rep. TRITA-NA-7302, 1973
[5] Deuflhard, P.: A Study of Discretization Schemes due to Hersch with Application to Stiff Differential Systems. Lecture given at the Oberwolfach Meeting on ?Numerical Treatment of Differential Equations?, July 4?July 10, 1976 (Unpublished)
[6] Deuflhard, P.: Order and Stepsize Control in Extrapolation Methods. Numer. Math.41, 399-422 (1983) · Zbl 0543.65049
[7] Deuflhard, P., Bader, G., Nowak, U.: LARKIN ? A Software Package for the Numerical Simulation of LARge Systems arising in Chemical Reaction KINetics. Springer Series chem. Phys.18, 38-55 (1981)
[8] Enright, W.H., Hull, T.E., Lindberg, B.: Comparing Numerical Methods for Stiff Systems of ODEs. BIT15, 10-48 (1975) · Zbl 0301.65040
[9] Garfinkel, D., Hess, B.: Metabolic Control Mechanisms VII. A Detailed Computer Model of the Glycolytic Pathway in Ascites Cells. J. Bio. Chem.239, 971-983 (1964)
[10] Gear, C.W.: Numerical Initial Value Problems in Ordinary Differential Equations. New York: Prentice Hall, 1971 · Zbl 1145.65316
[11] Gragg, W.B.: Repeated Extrapolation to the Limit in the Numerical Solution of Ordinary Differential Equations. University of California. Los Angeles: Thesis, 1963
[12] Gragg, W.B.: On Extrapolation Algorithms for Ordinary Initial Value Problems. SIAM J. Numer. Anal.2, 384-404 (1965) · Zbl 0135.37803
[13] Hindmarsh, A.C.: GEAR-Ordinary Differential Equation System Solver. Lawrence Livermore Laboratory: Tech. Rep. UCID-30001, Rev. 3 (Dec. 1974)
[14] Hofer, E.: A Partially Implicit Method for Large Stiff Systems of ODEs with only Few Equations Introducing Small Time-Constants. SIAM J. Numer. Anal.13, 645-663 (1976) · Zbl 0399.65043
[15] Kaps, P., Rentrop, P.: Generalized Runge-Kutta Methods of Order Four with Step Size Control for Stiff Ordinary Differential Equations. Numer. Math.33, 55-68 (1979) · Zbl 0436.65047
[16] Lawson, J.D.: Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants. SIAM J. Numer. Anal.4, 372-380 (1967) · Zbl 0223.65030
[17] Mirbeth, M.: Eine modifizierte Mittelpunktsregel zur numerischen Integration steifer Systeme von Differentialgleichungen. Technische Universität München, Institut für Mathematik: Diploma thesis, 1975
[18] Prothero, A., Robinson, A.: On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations. Math. Comput.28, 145-162 (1974) · Zbl 0309.65034
[19] Scott, M.R., Watts, H.A.: A Systematized Collection of Codes for Solving Two-Point Boundary-Value Problems. SANDIA Lab., Albuquerque: Tech. Rep. SAND 75-0539, 1975
[20] Shampine, L.F.: Evaluation of a Test Set for Stiff ODE Solvers. ACM TOMS7, 409-420 (1981)
[21] Sherman, A.H.: NSPIV-A FORTRAN Subroutine for Gaussian Elimination with Partial Pivoting. University of Texas at Austin: Tech. Rep. TR-65, CNA-118, 1977
[22] Stetter, H.J.: Symmetric Two-Step Algorithms for Ordinary Differential Equations. Comput.5, 267-280 (1970) · Zbl 0209.47001
[23] Stetter, H.J.: Analysis of Discretization Methods for Ordinary Differential Equations. Springer Tracts in Natural Philosophy. Berlin, Heidelberg, New York: Springer 1973
[24] Stoer, J., Bulirsch, R.: Einführung in die Numerische Mathematik II. Berlin, Heidelberg, New York: Springer, 1973 · Zbl 0257.65001
[25] Wilkinson, J.H.: The Algebraic Eigenvalue Problem. Clarendon, Oxford, 1965 · Zbl 0258.65037
[26] Hairer, E., Bader, G., Lubich, C.: On the Stability of Semi-Implicit Methods for Ordinary Differential Equations. BIT22, 211-232 (1982) · Zbl 0489.65046
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