Memory in a New Variant of King’s Family for Solving Nonlinear Systems

Munish Kansal, Alicia Cordero, Sonia Bhalla and Juan R. Torregrosa
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Munish Kansal: School of Mathematics, Thapar Institute of Engineering and Technology University, Patiala 147004, India
Alicia Cordero: Institute for Multidisciplinary Mathematics, Universitat Politècnica de Valenència, Camino de Vera s/n, 46022 València, Spain
Sonia Bhalla: Department of Mathematics, Chandigarh University, Gharuan 140413, India
Juan R. Torregrosa: Institute for Multidisciplinary Mathematics, Universitat Politècnica de Valenència, Camino de Vera s/n, 46022 València, Spain

Mathematics, 2020, vol. 8, issue 8, 1-15

Abstract: In the recent literature, very few high-order Jacobian-free methods with memory for solving nonlinear systems appear. In this paper, we introduce a new variant of King’s family with order four to solve nonlinear systems along with its convergence analysis. The proposed family requires two divided difference operators and to compute only one inverse of a matrix per iteration. Furthermore, we have extended the proposed scheme up to the sixth-order of convergence with two additional functional evaluations. In addition, these schemes are further extended to methods with memory. We illustrate their applicability by performing numerical experiments on a wide variety of practical problems, even big-sized. It is observed that these methods produce approximations of greater accuracy and are more efficient in practice, compared with the existing methods.

Keywords: nonlinear systems; convergence order; multi-point methods; schemes with memory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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