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On the design of high order exponentially fitted formulae for the numerical integration of stiff systems. (English) Zbl 0488.65028


MSC:

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

[1] Cash, J.R.: Stable recursions, with applications to the numerical solution of stiff systems. London: Academic Press, 1979 · Zbl 0498.65035
[2] Dahlquist, G., Lindberg, B.: On some implicit one-step methods for stiff differential equations. Report No. TRITA-NA 7304, Dept. of Information Processing, Royal Institute of Technology, Stockholm, Sweden
[3] Ehle, B.L.: On Padé approximations to the exponential function and A-stable methods for the numerical solution of initial value problems, Res. Rep. CSRR 2010, Dept. of Applied Analysis and Computer Science, Univ. of Waterloo, Ontario, Canada, 1969
[4] Iserles, A.: Functional fitting-new family of schemes for the integration of stiff O.D.E.. Math. Comput.31, 112-123 (1977) · Zbl 0348.65065
[5] Jackson, L.W., Kenue, S.K.: A fourth order exponentially fitted method. SIAM11 965-978 (1974) · Zbl 0319.65046
[6] Lambert, J.D.: Computational methods in ordinary differential equations. New York: John Wiley, 1973 · Zbl 0258.65069
[7] Lapidus, L., Schiesser, W.E.: Numerical methods for differential systems. New York: Academic Press, 1976 · Zbl 0624.65055
[8] Lindberg, B.: On a dangerous property of methods for stiff differential equations. BIT14, 430-436 (1974) · Zbl 0303.65066 · doi:10.1007/BF01932539
[9] Liniger, W., Willoughby, R.A.: Efficient integration methods for stiff systems of O.D.E.s. SIAM7, 47-66 (1970) · Zbl 0187.11003
[10] Stetter, H.J.: Analysis of discretization methods for ordinary differential equations. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0276.65001
[11] Willoughby, R.A.: Stiff differential systems. New York: Plenum Press, 1974 · Zbl 1261.65070
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