Abstract
The iterative multistep method (IMS) introduced by Hyman (1978) for solving initial value problems in ordinary differential equations has the advantage of being able to offer a higher degree of accuracy than the Runge-Kutta formulas by continuing the iteration process. In this article, another IMS formula is developed based on the geometric means predictor-corrector formulas introduced by Sanugi and Evans (1989). A numerical example is provided that shows that this formula can be used as a competitive alternative to Hyman's IMS formula.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hyman, J. M. (1978). Explicit A-Stable Iterative Methods for the Solution of Differential Equations, Report No. LA-UR-79-29, Los Alamos National Laboratory.
Hyman, J. M. (1979). A method of lines approach to the numerical solution of conservation of Laws, in Vichnevetsky, R., and Stepleman, R. S. (eds.),Advances in Computer Methods for Partial Differential Equations III, IMACS.
Sanugi, B. B., and Evans, D. J. (1989). New predictor-corrector trapezoidal formulae for solving initial value problems, in C. Brezinski (ed.),Numerical and Applied Mathematics, IMACS.
Sanugi, B. B. (1986). New Numerical Strategies for Initial Value Type Ordinary Differential Equations, Ph.D thesis, Loughborough University of Technology.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sanugi, B.B. An iterative multistep formula for solving initial value problems. J Sci Comput 7, 81–94 (1992). https://doi.org/10.1007/BF01060212
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01060212