A New Class of Iterative Processes for Solving Nonlinear Systems by Using One Divided Differences Operator

Mathematics

卷:7

Esther Sanabria¹  JuanR. Torregrosa²  Cristina Jordán²  Alicia Cordero² 

[1] Department of Applied Mathematics, Universitat Politènica de València, 46022 València, Spain;

[2] Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, Spain;

关键词: nonlinear systems;    multipoint iterative methods;    divided difference operator;    order of convergence;    Newton’s method;    computational efficiency index;   

DOI  :  10.3390/math7090776

来源: DOAJ

【 摘 要 】

In this manuscript, a new family of Jacobian-free iterative methods for solving nonlinear systems is presented. The fourth-order convergence for all the elements of the class is established, proving, in addition, that one element of this family has order five. The proposed methods have four steps and, in all of them, the same divided difference operator appears. Numerical problems, including systems of academic interest and the system resulting from the discretization of the boundary problem described by Fisher’s equation, are shown to compare the performance of the proposed schemes with other known ones. The numerical tests are in concordance with the theoretical results.

【 授权许可】

Unknown