Semi-Local Analysis and Real Life Applications of Higher-Order Iterative Schemes for Nonlinear Systems

Ramandeep Behl, Sonia Bhalla, Ioannis K. Argyros and Sanjeev Kumar
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Ramandeep Behl: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Sonia Bhalla: Department of Mathematics, Chandigarh University, Gharuan 140413, Mohali, Punjab, India
Ioannis K. Argyros: Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
Sanjeev Kumar: School of Mathematics, Thapar Institute of Engineering and Technology University, Patiala 147004, Punjab, India

Mathematics, 2020, vol. 8, issue 1, 1-14

Abstract: Our aim is to improve the applicability of the family suggested by Bhalla et al. (Computational and Applied Mathematics, 2018) for the approximation of solutions of nonlinear systems. Semi-local convergence relies on conditions with first order derivatives and Lipschitz constants in contrast to other works requiring higher order derivatives not appearing in these schemes. Hence, the usage of these schemes is improved. Moreover, a variety of real world problems, namely, Bratu’s 1D, Bratu’s 2D and Fisher’s problems, are applied in order to inspect the utilization of the family and to test the theoretical results by adopting variable precision arithmetics in Mathematica 10. On account of these examples, it is concluded that the family is more efficient and shows better performance as compared to the existing one.

Keywords: computational efficiency; system of nonlinear equations; semi-local convergence analysis; Steffensen’s method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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