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...

Full description

Saved in:
Bibliographic Details
Main Author: J. P. Jaiswal
Format: Article
Language:English
Published: Wiley 2015-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2015/938606
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850179713246429184
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