Two Bi-Accelerator Improved with Memory Schemes for Solving Nonlinear Equations
The present paper is devoted to the improvement of the R-order convergence of with memory derivative free methods presented by Lotfi et al. (2014) without doing any new evaluation. To achieve this aim one more self-accelerating parameter is inserted, which is calculated with the help of Newton’s int...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/938606 |
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| Summary: | The present paper is devoted to the improvement of the R-order convergence of with memory derivative free methods presented by Lotfi et al. (2014) without doing any new evaluation. To achieve this aim one more self-accelerating parameter is inserted, which is calculated with the help of Newton’s interpolatory polynomial. First theoretically it is proved that the R-order of convergence of the proposed schemes is increased from 6 to 7 and 12 to 14, respectively, without adding any extra evaluation. Smooth as well as nonsmooth examples are discussed to confirm theoretical result and superiority of the proposed schemes. |
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| ISSN: | 1026-0226 1607-887X |