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On the integration of stiff systems of O.D.E.s using extended backward differentiation formulae. (English) Zbl 0411.65040


MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations

Software:

GEAR; DIFSUB
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Full Text: DOI EuDML

References:

[1] Alexander, R.: Diagonally implicit Runge-Kutta methods. SIAM J. Numer. Anal.14, 1006-1022 (1977) · Zbl 0374.65038 · doi:10.1137/0714068
[2] Butcher, J.C.: Implicit Runge-Kutta processes. Math. Comp.18, 50-64 (1964) · Zbl 0123.11701 · doi:10.1090/S0025-5718-1964-0159424-9
[3] Butcher, J.C.: Integration processes based on Radau quadrature formulas. Math. Comp.18, 233-244 (1964) · Zbl 0123.11702 · doi:10.1090/S0025-5718-1964-0165693-1
[4] Cash, J.R.: Stable recursions, with applications to the numerical solution of stiff systems. London, New York: Academic Press 1979 · Zbl 0498.65035
[5] Ehle, B.L.: High orderA-stable methods for the numerical solution of differential equations. BIT8, 276-278 (1968) · Zbl 0176.14604 · doi:10.1007/BF01933437
[6] Enright, W.H., Hull, T.E.: Numerical methods for the solution of stiff systems. In: Numerical methods for Differential systems. (L. Lapidus, W.E. Schiesser, eds.), pp.45-63. London-New York: Academic Press 1976 · Zbl 0355.65057
[7] Gear, C.W.: Algorithm 407, Difsub for solution of ordinary differential equations, Comm. ACM14, 185-190 (1971) · doi:10.1145/362566.362573
[8] Hindmarsh, A.C.: GEAR: Ordinary differential equation system solver, UCID-30001, Rev. 3, Lawrence Livermore Laboratory, Univ. of California, Livermore, 1974
[9] Krogh, F.T.: VODQ/SVDQ/DVDQ-variable order integrators for the numerical solution of ordinary differential equations. TU Doc. No. CP-2308, NPO 11643, JPL California, 1969
[10] Lambert, J.D.: Computational methods in ordinary differential equations. New York: Wiley, 1973 · Zbl 0258.65069
[11] Liniger, W., Willoughby, R.A.: Efficient numerical integration of stiff systems of ordinary differential equations. Technical Report RC-1970, Thomas J. Watson Research Center, Yorktown Heights, N. Y. 1967 · Zbl 0187.11003
[12] Robertson, H.H.: The solution of a set of reaction rate equations. In: Numerical analysis ? an introduction, (J. Walsh, ed.), pp. 178-182. London, New York: Academic Press 1966
[13] Rosenbrock, H.H.: Some general implicit processes for the numerical solution of differential equations. Comput. J.,5, 329-330 (1963) · Zbl 0112.07805 · doi:10.1093/comjnl/5.4.329
[14] Shampine, L.F., Gordon, M.K.: Computer solution of ordinary differential equations, San Francisco: W.H. Freeman 1975 · Zbl 0347.65001
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