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

Alicia Cordero, Cristina Jordán, Esther Sanabria and Juan R. Torregrosa
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Alicia Cordero: Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, Spain
Cristina Jordán: Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, Spain
Esther Sanabria: Department of Applied Mathematics, Universitat Politènica de València, 46022 València, Spain
Juan R. Torregrosa: Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, Spain

Mathematics, 2019, vol. 7, issue 9, 1-12

Abstract: 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.

Keywords: nonlinear systems; multipoint iterative methods; divided difference operator; order of convergence; Newton’s method; computational efficiency index (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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