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In this paper, a new numerical method of finding the roots of a nonlinear system is proposed, which extends the conventional fixed point iterative method by relaxing the constraints on it. The proposed method determines the real valued roots and expands the convergence region by relaxing the constraints on the conventional fixed point iterative method, which transforms the diverging root searching iterations into the converging iterations by employing the metric induced by the geometrical characteristics of a polynomial. A metric is set to measure the distance between a point of a real-valued function and its corresponding image point of its inverse function. The proposed scheme provides the convenience in finding not only the real roots of polynomials but also the roots of the nonlinear systems in the various application areas of science and engineering.
목차
Abstract
1. Introduction
2. Problems Involved in CFPT
3. Extended Contractive Iteration Method (ECIM)
4. Numerical Simulations
5. Conclusions
References
참고문헌 (7)
참고문헌 신청
S. Banach, “Sur Les operations dans les ensembles abstraits et leur application aux equations integrales,” Fundamenta Mathematicae No. 3, pp. 133-181, 1992.
Lj. B. iri, “A generalization of Banach’s contraction principle,” Proc. Amer. Math. Soc., No. 45, pp. 267-273, 1974.
G. Jungck, “Computing mappings and fixed points,” Proc. Amer. Math. Monthly, 83, No. 4, pp. 261-263, 1976.
M. Saqib, M. Iqbal, S. Ahmed, S. Ali, T. Iamaeel, “New modification of fixed point iterative method for solvinf nonlinear equations,” Applied Mathematics, Monthly, No. 6, pp. 1857-1863, 2015.
Noor, M. A. and Inayat, K., “Fifth-order Iterative Methods for Solving Nonlinear Equations,” Applied Mathematics and Computation, No. 188, pp. 406-410, 2017.
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