A variant of the Newton-Kantorovich theorem for nonlinear integral equations of mixed Hammerstein type

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• 作者：J.A. Ezquerro ; ^{jezquer@unirioja.es} ; D. Gonzá ; lez ^{daniel.gonzalez@unirioja.es} ; M.A. Herná ; ndez ^{mahernan@unirioja.es}
• 关键词：Hammerstein&rsquo ; s equation ; Bratu&rsquo ; s equation ; Newton&rsquo ; s method ; Kantorovich&rsquo ; s theorem ; Semilocal convergence ; Majorizing sequence
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：15 May, 2012
• 卷：218
• 期：18
• 页码：9536-9546
• 文件大小：349 K

摘要

We study nonlinear integral equations of mixed Hammerstein type using Newton鈥檚 method as follows. We investigate the theoretical significance of Newton鈥檚 method to draw conclusions about the existence and uniqueness of solutions of these equations. After that, we approximate the solutions of a particular nonlinear integral equation by Newton鈥檚 method. For this, we use the majorant principle, which is based on the concept of majorizing sequence given by Kantorovich, and milder convergence conditions than those of Kantorovich. Actually, we prove a semilocal convergence theorem which is applicable to situations where Kantorovich鈥檚 theorem is not.