Local convergence of a family of iterative methods for Hammerstein equations

被引：0
作者：
Eulalia Martínez
Sukhjit Singh
José L. Hueso
Dharmendra K. Gupta
机构：
[1] Universitat Politècnica de València,Instituto Universitario de Matemática Multidisciplinar
[2] Indian Institute of Technology Kharagpur,Department of Mathematics
[3] Universitat Politècnica de València,Instituto Universitario de Matemática Pura y Aplicada
来源：
Journal of Mathematical Chemistry | 2016年 / 54卷
关键词：
Nonlinear systems; Iterative method; Banach space ; Local convergence; Complex dynamics; Hammerstein equation; 47H99; 65H10;
D O I：
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中图分类号：
学科分类号：
摘要：
In this paper we give a local convergence result for a uniparametric family of iterative methods for nonlinear equations in Banach spaces. We assume boundedness conditions involving only the first Fréchet derivative, instead of using boundedness conditions for high order derivatives as it is usual in studies of semilocal convergence, which is a drawback for solving some practical problems. The existence and uniqueness theorem that establishes the convergence balls of these methods is obtained. We apply this theory to different examples, including a nonlinear Hammerstein equation that have many applications in chemistry and appears in problems of electro-magnetic fluid dynamics or in the kinetic theory of gases. With these examples we illustrate the advantages of these results. The global convergence of the method is addressed by analysing the behaviour of the methods on complex polynomials of second degree.
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页码：1370 / 1386
页数：16
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