New Two-step Iterative Methods for Solving Nonlinear Equations

Mohamed S. M. Bahgat

Abstract


In this paper, we have suggested and analyzed a new two-step type iterative methods for solving nonlinear equations of the type. We show that this new two-step method is cubic convergence method. It is proved that this method is better than the Newton method and all results in (Soheili et al., 2008). Several examples are given to illustrate the efficiency of this new method and its comparison with other methods. This method can se considered as a significant improvement of the Newton method and its variant forms.


Full Text:

PDF


DOI: https://doi.org/10.5539/jmr.v4n3p128


This work is licensed under a Creative Commons Attribution 4.0 International License.

Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

Copyright © Canadian Center of Science and Education

To make sure that you can receive messages from us, please add the 'ccsenet.org' domain to your e-mail 'safe list'. If you do not receive e-mail in your 'inbox', check your 'bulk mail' or 'junk mail' folders.

----------------------------------------------------------------------------------------------------------------------------------------------------------------------
{"cc_re__cc_re__cc_by_4_0": ["rms. \"/>\n\t<meta name=\"DC.Format\" scheme=\"IMT\" content=\"application/pdf\"/>\n\t<meta name=\"DC.Identifier\" content=\"16156\"/>\n\t<meta name=\"DC.Identifier.pageNumber\" content=\"p128\"/>\n\t\t\t\t\t\t\t<meta name=\"DC.Identifier.DOI\" content=\"10.5539/jmr.v4n3p128\"/>\n\t\t<meta name=\"DC.Identifier.URI\" content=\"http://ccsenet.org/journal/index.php/jmr/article/view/16156\"/>\n\t<meta name=\"DC.Language\" scheme=\"ISO639-1\" content=\"en\"/>\n\t<meta name=\"DC.Rights\" content=\"Copyright (c) 2016 Journal of Mathematics Research\" />\n\t<meta name=\"DC.Rights\" content=\"http://creativecommons.org/licenses/by/4.0\"/>\n\t<meta name=\"DC.Source\" content=\"Journal of Mathematics Research\"/>\n\t<meta name=\"DC.Source.ISSN\" content=\"1916-9809\"/>\n\t<meta name=\"DC.Source.Issue\" content=\"3\"/>\t<meta name=\"DC.Source.URI\" content=\"http://ccsenet.org/journal/index.php/jmr\"/>\n\t<meta name=\"DC.Source.Volume\" content=\"4\"/>\t<meta name=\"DC.Title\" content=\"New Two-step Iterative Methods for Solving Nonlinear Equations\"/>\n\t\t<meta name=\"DC.Type\" content=\"Text.Serial.Journal\"/>\n\t<meta name=\"DC.Type.articleType\" content=\"Articles\"/>\n\t\t<m", "onsidered as a significant improvement of the Newton method and its variant forms.</p></div>\n\t\t<br />\n\t\t</div>\n\t\n\t\n\t\t\t\t\n\t\t\t<div id=\"articleFullText\">\n\t\t<h4>Full Text:</h4>\n\t\t\t\t\t\t\t\t\t<a href=\"http://ccsenet.org/journal/index.php/jmr/article/view/16156/11874\" class=\"file\" target=\"_parent\">PDF</a>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t</div>\n\t\n\t\n\t\t\t\t\t\t\t<br />\n\t\t<br />\n\t\tDOI: <a id=\"pub-id::doi\" href=\"https://doi.org/10.5539/jmr.v4n3p128\">https://doi.org/10.5539/jmr.v4n3p128</a>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\n\n\n\t\t\t\t<br /><br />\n\t\t\t\t\t<a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"http://i.creativecommons.org/l/by/4.0/88x31.png\" /></a><br />This work is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\">Creative Commons Attribution 4.0 International License</a>.\n\t\t\t\n\n<br /><br />\n<p>Journal of Mathematics Research\u00a0\u00a0 ISSN 1916-9795 (Print)\u00a0\u00a0 ISSN 1916-9809 (Online)</p><p>Copyright \u00a9 Canadian Center of Science and Education</p><p>To make sure that you can receive messages ", "php/jmr/article/view/16156/11874\" class=\"file\" target=\"_parent\">PDF</a>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t</div>\n\t\n\t\n\t\t\t\t\t\t\t<br />\n\t\t<br />\n\t\tDOI: <a id=\"pub-id::doi\" href=\"https://doi.org/10.5539/jmr.v4n3p128\">https://doi.org/10.5539/jmr.v4n3p128</a>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\n\n\n\t\t\t\t<br /><br />\n\t\t\t\t\t<a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"http://i.creativecommons.org/l/by/4.0/88x31.png\" /></a><br />This work is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\">Creative Commons Attribution 4.0 International License</a>.\n\t\t\t\n\n<br /><br />\n<p>Journal of Mathematics Research\u00a0\u00a0 ISSN 1916-9795 (Print)\u00a0\u00a0 ISSN 1916-9809 (Online)</p><p>Copyright \u00a9 Canadian Center of Science and Education</p><p>To make sure that you can receive messages from us, please add the 'ccsenet.org' domain to your e-mail 'safe list'. If you do not receive e-mail in your 'inbox', check your 'bulk mail' or 'junk mail' folders.</p><p>---------------------------------------------------"], "copyright__copyright__copyright": ["hematics Research\u00a0\u00a0 ISSN 1916-9795 (Print)\u00a0\u00a0 ISSN 1916-9809 (Online)\n\nCopyright \u00a9 Canadian Center of Science and Education\n\nTo make sure that you can receive messages from us, please add the 'ccsenet.org' domain to your e-mail 'safe list'. If you do not receive e-mail in your 'inbox', check your 'bulk mail' or 'junk mail' folders.\n\n----------------------------------------------------------------------------------------------------------------------------------------------------------------------", "hematics Research\u00a0\u00a0 ISSN 1916-9795 (Print)\u00a0\u00a0 ISSN 1916-9809 (Online)\n\nCopyright \u00a9 Canadian Center of Science and Education\n\nTo make sure that you can receive messages from us, please add the 'ccsenet.org' domain to your e-mail 'safe list'. If you do not receive e-mail in your 'inbox', check your 'bulk mail' or 'junk mail' folders.\n\n----------------------------------------------------------------------------------------------------------------------------------------------------------------------", "hematics Research\u00a0\u00a0 ISSN 1916-9795 (Print)\u00a0\u00a0 ISSN 1916-9809 (Online)\n\nCopyright \u00a9 Canadian Center of Science and Education\n\nTo make sure that you can receive messages from us, please add the 'ccsenet.org' domain to your e-mail 'safe list'. If you do not receive e-mail in your 'inbox', check your 'bulk mail' or 'junk mail' folders.\n\n----------------------------------------------------------------------------------------------------------------------------------------------------------------------", "hematics Research\u00a0\u00a0 ISSN 1916-9795 (Print)\u00a0\u00a0 ISSN 1916-9809 (Online)\n\nCopyright \u00a9 Canadian Center of Science and Education\n\nTo make sure that you can receive messages from us, please add the 'ccsenet.org' domain to your e-mail 'safe list'. If you do not receive e-mail in your 'inbox', check your 'bulk mail' or 'junk mail' folders.\n\n----------------------------------------------------------------------------------------------------------------------------------------------------------------------"]}