On a Bi-Parametric Family of Fourth Order Composite Newton–Jarratt Methods for Nonlinear Systems

Janak Raj Sharma, Deepak Kumar, Ioannis K. Argyros and Ángel Alberto Magreñán
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Janak Raj Sharma: Department of Mathematics, Sant Longowal Institute of Engineering and Technology Longowal, Sangrur 148106, India
Deepak Kumar: Department of Mathematics, Sant Longowal Institute of Engineering and Technology Longowal, Sangrur 148106, India
Ioannis K. Argyros: Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA
Ángel Alberto Magreñán: Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, La Rioja, Spain

Mathematics, 2019, vol. 7, issue 6, 1-27

Abstract: We present a new two-parameter family of fourth-order iterative methods for solving systems of nonlinear equations. The scheme is composed of two Newton–Jarratt steps and requires the evaluation of one function and two first derivatives in each iteration. Convergence including the order of convergence, the radius of convergence, and error bounds is presented. Theoretical results are verified through numerical experimentation. Stability of the proposed class is analyzed and presented by means of using new dynamics tool, namely, the convergence plane. Performance is exhibited by implementing the methods on nonlinear systems of equations, including those resulting from the discretization of the boundary value problem. In addition, numerical comparisons are made with the existing techniques of the same order. Results show the better performance of the proposed techniques than the existing ones.

Keywords: nonlinear equations; Newton method; Jarratt method; convergence; complex dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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