Some High-Order Iterative Methods for Nonlinear Models Originating from Real Life Problems

Malik Zaka Ullah, Ramandeep Behl and Ioannis K. Argyros
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Malik Zaka Ullah: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Ramandeep Behl: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Ioannis K. Argyros: Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

Mathematics, 2020, vol. 8, issue 8, 1-17

Abstract: We develop a sixth order Steffensen-type method with one parameter in order to solve systems of equations. Our study’s novelty lies in the fact that two types of local convergence are established under weak conditions, including computable error bounds and uniqueness of the results. The performance of our methods is discussed and compared to other schemes using similar information. Finally, very large systems of equations ( 100 × 100 and 200 × 200 ) are solved in order to test the theoretical results and compare them favorably to earlier works.

Keywords: local convergence; Steffensen’s method; Banach space; system of equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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