This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Ahlfors, L.V., Complex Analysis, McGraw-Hill, New York, 1953.
Ansell, H.G., On certain two-variable generalizations of circuit theory, with applications to networks of transmission lines and lumped reactances, IEEE Trans. on C.T. 11, (1964), 214–223.
Bickart, T.A., D.A. Burgess and H.M. Sloate, High order A-stable composite multistep methods for numerical integration of stiff differential equations, in Proc. 9th Annual Allerton Conf. on Circuit and System Theory, (1971), 465–473.
Dahlquist, G., Convergence and stability in the numerical integration of ordinary differential equations, Trans. Roy. Inst. Tech., Stockholm, Nr. 130, 1959.
_____, A special stability problem for linear multistep methods, BIT 3, (1963), 27–43.
Daniel, J.W. and R.E. Moore, Computation and theory in ordinary differential equations, Freeman and Co., San Francisco, 1970.
Ehle, B.L., High order A-stable methods for the numerical solution of systems of D.E.’s, BIT 8, (1968), 276–278.
Genin, Y., An algebraic approach to A-stable linear multistep-multiderivative integration formulas, BIT 14, (1974), 382–406.
Griepentrog, E., Mehrschrittverfahren zur numerischen Integration von gewöhnlichen Differentialgleichungssystemen und asymptotische Exaktheit, Wiss. Z. Humboldt-Univ. Berlin Math.-Natur. Reihe, v. 19, (1970), 637–653.
Henrici, P., Discrete variable methods in ordinary differential equations, Wiley, New York, 1962.
Jeltsch, R., Integration of iterated integrals by multistep methods, Numer. Math. 21, (1973), 303–316.
Jeltsch, R., A necessary condition for A-stability of multistep multiderivative methods, to appear in Math. Comp., 30 (1976).
Jeltsch, R., Stiff stability of multistep multiderivative methods, to appear in SIAM J. on numer. Anal.
Jeltsch, R., Multistep multiderivative methods for the numerical solution of initial value problems of ordinary differential equations., Seminar Notes 1975/76, University of Kentucky, 1976.
Nevanlinna, O. and A.H. Sipilä, A nonexistence theorem for explicit A-stable methods, Math. Comp., 28 (1974), 1053–1055.
Reimer, M., Finite difference forms containing derivatives of higher order, SIAM J. Numer. Anal., 5 (1968), 725–738.
Rubin, W.B., A-stability and composite multistep methods, Ph. D. Thesis, EE Dept., Syracuse University, New York, 1973.
Sloate, H.M. and T.A. Bickart, A-stable composite multistep methods, JACM 20, (1973), 7–26.
Stetter, H.J., Analysis of discretization methods of ordinary differential equations, Springer, New York, 1973.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1978 Springer-Verlag
About this paper
Cite this paper
Jeltsch, R. (1978). On the stability regions of multistep multiderivative methods. In: Bulirsch, R., Grigorieff, R.D., Schröder, J. (eds) Numerical Treatment of Differential Equations. Lecture Notes in Mathematics, vol 631. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067464
Download citation
DOI: https://doi.org/10.1007/BFb0067464
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08539-3
Online ISBN: 978-3-540-35970-8
eBook Packages: Springer Book Archive
