Steffensen type methods for approximating solutions of differential equations

Abstract

The implicit methods for numerical solving of ODEs lead to nonlinear equations which are usually solved by the Newton method. We study the use of a Steffensen type method instead, and we give conditions under which this method provides bilateral approximations for the solution of these equations; this approach offers a more rigorous control of the errors. Moreover, the method can be applied even in the case when certain functions are not differentiable on the definition domain. The convergence order is the same as for Newton method.

Authors

Flavius Patrulescu
(Tiberiu Popoviciu Institute of Numerical Analysis,
Romanian Academy)

Keywords

initial value problems; stiff equations; Steffensen method; Newton method; convergence order

Cite this paper as

F. Pătrulescu, Steffensen type methods for approximating solutions of differential equations, Studia Universitatis Babeş-Bolyai, seria Mathematica, vol. 56, no. 2 (2011), pp. 505-515.

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About this paper

Publisher Name

Universitatea Babeş-Bolyai, Cluj-Napoca; Cluj University Press, Cluj-Napoca

Print ISSN

0252-1938

Online ISSN

2065-961x

MR

2843708

ZBL

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