A note on the convergence of solutions of certain second order differential equations
Ezeilo, J.O.C. (1965)
Portugaliae mathematica
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Ezeilo, J.O.C. (1965)
Portugaliae mathematica
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D. Edelen (1978)
Banach Center Publications
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Ioannis K. Argyros, Santhosh George (2017)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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This paper is devoted to the study of a multi-step method with divided differences for solving nonlinear equations in Banach spaces. In earlier studies, hypotheses on the Fréchet derivative up to the sixth order of the operator under consideration is used to prove the convergence of the method. That restricts the applicability of the method. In this paper we extended the applicability of the sixth-order multi-step method by using only hypotheses on the first derivative of the operator...
Norman Levinson (1949)
Colloquium Mathematicae
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Maria Contessa, Fabio Zanolin (1977)
Rendiconti del Seminario Matematico della Università di Padova
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Santhosh George, Ioannis K. Argyros (2019)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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The aim of this article is to provide the local convergence analysis of two novel competing sixth convergence order methods for solving equations involving Banach space valued operators. Earlier studies have used hypotheses reaching up to the sixth derivative but only the first derivative appears in these methods. These hypotheses limit the applicability of the methods. That is why we are motivated to present convergence analysis based only on the first derivative. Numerical examples...
Hassan Nasr Ahmed Ismail (1979)
Aplikace matematiky
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This paper is the continuation of the paper "Generalized periodic overimplicit multistep methods" of the same author and it deals with the necessary and, in some special cases, with the necessary and sufficient conditions for the convergence of general periodic overimplicit multistep methods.