A free-derivative iteration method of order three having convergence of both point and interval for nonlinear equations (Q1406053)
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scientific article; zbMATH DE number 1977923
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A free-derivative iteration method of order three having convergence of both point and interval for nonlinear equations |
scientific article; zbMATH DE number 1977923 |
Statements
A free-derivative iteration method of order three having convergence of both point and interval for nonlinear equations (English)
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9 September 2003
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A new iterative formulae containing only the values of a nonlinear function \(f\) is proposed to compute the both sequences, \(\{ x_n\}\) and \(\{[a_n,b_n]\}\), converging cubically to the unique zero of \(f\). The numerical results show that the proposed algorithm leads to solution in certain cases where the Newton or Steffensen method fails.
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nonlinear equations
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deviative-free method
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comparison of methods
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Newton emthod
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numerical results
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algorithm
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Steffensen method
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free-derivative iteration method
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convergence
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