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An A-stable modification of the Adams-Bashforth methods

Part of the Lecture Notes in Mathematics book series (LNM,volume 109)

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

  1. G.G. DAHLQUIST. A special stability problem for linear multistep methods, BIT 3 (1963) pp. 27–43.

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  5. 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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04628-8

  • Online ISBN: 978-3-540-36158-9

  • eBook Packages: Springer Book Archive