On the local convergence of a two-step combined Newton-secan-Kurchatov type method under two different continuity conditions
Charmita Pradhan, Nishant Kumar, Jai Prakash Jaiswal
Department of Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur, Chhattisgarh, India
Keywords: nondifferentiable operator, local convergence, convergence order, Lipschitz condition, L-average condition
Abstract
In this paper, we explore a double-step method for solving nonlinear equations containing a differentiable and non-differentiable operator. Our approach is built upon a combination of three different methods. We have analyzed the local convergence of the suggested method, considering both Lipschitz and L-average conditions & established the superquadratic (≈ 2.414) order of convergence. Finally we have pictured numerical results in comparison with several existing methods.
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