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Open AccessArticle

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

1
Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2
Department of Mathematics, Chandigarh University, Gharuan 140413, Mohali, Punjab, India
3
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
4
School of Mathematics, Thapar Institute of Engineering and Technology University, Patiala 147004, Punjab, India
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 92; https://doi.org/10.3390/math8010092
Received: 25 November 2019 / Revised: 22 December 2019 / Accepted: 31 December 2019 / Published: 6 January 2020
(This article belongs to the Special Issue Computational Methods in Analysis and Applications 2020)
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. View Full-Text
Keywords: computational efficiency; system of nonlinear equations; semi-local convergence analysis; Steffensen’s method computational efficiency; system of nonlinear equations; semi-local convergence analysis; Steffensen’s method
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Behl, R.; Bhalla, S.; Argyros, I.K.; Kumar, S. Semi-Local Analysis and Real Life Applications of Higher-Order Iterative Schemes for Nonlinear Systems. Mathematics 2020, 8, 92.

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