Abstract
This paper gives new finite difference formulae which are suitable for the numerical integration of stiff systems of ordinary differential equations. The method is exact if the problem is of the type y1 = Py + Q(x) where P is a constant and Q(x) a polynomial of degree q. When P = 0 the method is identical with the Adams-Bashforth formulae.
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References
G.G. DAHLQUIST. A special stability problem for linear multistep methods, BIT 3 (1963) pp. 27–43.
P. HENRICI, Discrete variable methods in ordinary differential equations, John Wiley and Sons, Inc., New York, London, 1962.
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C.W. GEAR, Numerical integration of still ordinary differential equations, Report No. 221, University of Illinois, Department of Computer Science (January, 1967).
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© 1969 Springer-Verlag
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Norsett, S.P. (1969). An A-stable modification of the Adams-Bashforth methods. In: Morris, J.L. (eds) Conference on the Numerical Solution of Differential Equations. Lecture Notes in Mathematics, vol 109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060031
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DOI: https://doi.org/10.1007/BFb0060031
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