Local convergence analysis of two competing two-step iterative methods free of derivatives for solving equations and systems of equations

Ioannis K. Argyros, Santhosh George

Abstract


We present the local convergence analysis of two-step iterative methods free of derivatives for solving equations and systems of equations under similar hypotheses based on Lipschitz-type conditions. The methods are in particular useful for solving equations or systems involving non-differentiable terms. A comparison is also provided using suitable numerical examples.


Keywords


Two-step secant method, two-step Kurchatov method, local convergence, divided differences, Fr\'echet-derivative, radius of convergence, Lipschitz conditions

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ISSN: 1331-0623 (Print), 1848-8013 (Online)