Abstract

FAMILIES OF QUADRATURE-BASED ITERATIVE METHODS FOR SOLVING NONLINEAR SYSTEMS OF EQUATIONS

1Oghovese Ogbereyivwe and 2Kingsley O. Muka

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Abstract In this paper, two-step and three-step families of iterative methods for approximating the zero of nonlinear system of equations of convergence order ??6 are proposed by modifying the three-step quadrature based methods of convergence order ?=4 in Noor et al., [10]. The convergence of the proposed families of iterative methods is proved using the Taylor’s series technique. Computational efficiencies of the proposed methods are considered and compared with methods from which they are derived. The numerical results generated by methods proposed compared with methods from which they have been developed, shows that methods developed herein do not onlyconfirm theoretical results, but also are efficient and adequate in approximating zero of nonlinear system of equations. Keywords: Iterative methods, quadrature based methods, efficiency index.

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