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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| Format: | Article |
| Language: | English |
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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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| author | J. P. Jaiswal |
| author_facet | J. P. Jaiswal |
| author_sort | J. P. Jaiswal |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-99a03bbe6314490aae8a0e2e45b7a43c |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-99a03bbe6314490aae8a0e2e45b7a43c2025-08-20T02:18:25ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/938606938606Two Bi-Accelerator Improved with Memory Schemes for Solving Nonlinear EquationsJ. P. Jaiswal0Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, Madhya Pradesh 462051, IndiaThe 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.http://dx.doi.org/10.1155/2015/938606 |
| spellingShingle | J. P. Jaiswal Two Bi-Accelerator Improved with Memory Schemes for Solving Nonlinear Equations Discrete Dynamics in Nature and Society |
| title | Two Bi-Accelerator Improved with Memory Schemes for Solving Nonlinear Equations |
| title_full | Two Bi-Accelerator Improved with Memory Schemes for Solving Nonlinear Equations |
| title_fullStr | Two Bi-Accelerator Improved with Memory Schemes for Solving Nonlinear Equations |
| title_full_unstemmed | Two Bi-Accelerator Improved with Memory Schemes for Solving Nonlinear Equations |
| title_short | Two Bi-Accelerator Improved with Memory Schemes for Solving Nonlinear Equations |
| title_sort | two bi accelerator improved with memory schemes for solving nonlinear equations |
| url | http://dx.doi.org/10.1155/2015/938606 |
| work_keys_str_mv | AT jpjaiswal twobiacceleratorimprovedwithmemoryschemesforsolvingnonlinearequations |