Local convergence of a fifth-order Newton-type iterative method for solving systems of nonlinear equations

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Abstract
Based on the Lipschitz continuity condition, we study the local convergence analysis of a fifth-order Newton-type iterative method to solve nonlinear equations in Banach spaces. Lipschitz continuity condition on the first derivative is assumed to broaden the applicability of the method. Our study provides a thorough local convergence analysis in Banach spaces, including radii of convergence balls, computable error bounds, and the uniqueness of the solution. Finally, numerical experiments on various nonlinear models confirm the theoretical convergence criteria.

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