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

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 first-order Frechet derivative to ensure the convergence and provides the uniqueness...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 12; no. 1; p. 314
Main Authors Sharma, Debasis, Parhi, Sanjaya Kumar
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.01.2022
Elman Hasanoglu
Subjects
Banach spaces
Convergence
Error analysis
Functional equations
Functions
Iterative methods (Mathematics)
Mathematical research
Nonlinear systems
Polynomials
Software
India
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ISSN2146-1147
2146-1147

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Summary: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 first-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 effective. 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 beneficial when prior studies fail to solve problems. Keywords: Local convergence, Iterative methods, Banach space, Lipschitz continuity condition, Basin of attraction AMS Subject Classification: 47H99, 49M15, 65D99, 65G99, 65J15
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ISSN:2146-1147
2146-1147