Abstract
Using a known interpolation formula we introduce a class of numerical methods for approximating the solutions of scalar initial value problems for first order differential equations, which can be identified as explicit Runge-Kutta methods. We determine bounds for the local truncation error and we also compare the convergence order and the stability region with those for explicit Runge-Kutta methods, which have convergence order equal with number of stages (i.e. with 2, 3 and 4 stages). The convergence order is only two, but our methods have a larger absolute stability region than the above mentioned methods. In the last section a numerical example is provided, and the obtained numerical approximation is compared with the corresponding exact solution.
Authors
Flavius Patrulescu
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)
Keywords
initial value problem; stability region; convergence order; local truncation error
Cite this paper as
F. Pătrulescu, A numerical method for the solution of an autonomous initial value problem, Carpathian J. Math. vol. 28 (2012), pp. 289-296
About this paper
Journal
Carpathian Journal of Mathematics
Publisher Name
North University of Baia Mare, Department of Mathematics and Computer Science, Baia Mare
Print ISSN
1584-2851
Online ISSN
1843-4401
MR
3027258
ZBL
1289.65153
Google Scholar
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