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- Title
Steffensen type methods for approximating solutions of differential equations.
- Authors
Părulescu, Flavius
- 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 con- ditions under which this method provides bilateral approximations for the solution of these equations; this approach offers a more rigorous con- trol 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.
- Subjects
DIFFERENTIAL equations; APPROXIMATION theory; NEWTON-Raphson method; STOCHASTIC convergence; INITIAL value problems; STIFF computation (Differential equations)
- Publication
Studia Universitatis Babeş-Bolyai, Mathematica, 2011, Vol 56, Issue 2, p505
- ISSN
0252-1938
- Publication type
Article