EXTENDING THE APPLICABILITY OF A FOURTH-ORDER METHOD UNDER LIPSCHITZ CONTINUOUS DERIVATIVE IN BANACH SPACES

EXTENDING THE APPLICABILITY OF A FOURTH-ORDER METHOD UNDER LIPSCHITZ CONTINUOUS DERIVATIVE IN BANACH SPACES/h2>

D. Sharma, S. K. Parhi

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Abstract

We extend the applicability of a fourth-order convergent nonlinear system solver by providing its local convergence analysis under Lipschitz continuous Frechet derivative in Banach spaces. Our analysis only uses the rst-order Frechet derivative to ensure the convergence and provides the uniqueness of the solution, the radius of convergence ball and the computable error bounds. This study is applicable in solving such problems for which earlier studies are not eective. Furthermore, the convergence region for the scheme to approximate the zeros of various polynomials is studied using basins of attraction tool. Various computational tests are conducted to validate that our analysis is benecial when prior studies fail to solve problems.

Keywords

Local convergence, Iterative methods, Banach space, Lipschitz continuity condition, Basin of attraction