Two new three-step predictor-corrector methods with fifth-order convergence for solving nonlinear equations

In this paper, we present two new three-step predictor-corrector methods for solving nonlinear equations. This two algorithms are free from second derivative and per iteration they only require three evaluations of the given function and one evaluation of its first derivative. Convergence analysis s...

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Bibliographic Details
Published in2010 Second International Conference on Computational Intelligence and Natural Computing Vol. 2; pp. 16 - 19
Main Authors Yunhong Hu, Liang Fang, Guoping He
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.09.2010
Subjects
Convergence
Iterative methods
Newton method
Newton's method
Nonlinear equations
Prediction algorithms
predictor-corrector type iterative method
three-step method
two-step method
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Summary:In this paper, we present two new three-step predictor-corrector methods for solving nonlinear equations. This two algorithms are free from second derivative and per iteration they only require three evaluations of the given function and one evaluation of its first derivative. Convergence analysis shows that they are fifth-order convergent. Numerical tests demonstrate that both of the two new methods are more efficient and more practical than most of known variants of two-step methods.
ISBN:9781424477050
1424477050
DOI:10.1109/CINC.2010.5643799