The Newton-Kantorovich method in theory of nonlinear intergo-differential boundary value problem

Chechetenko V. O.; Chuiko Oleksiy Serhiyovych; Chuiko Sergey Mykhailovych

doi:https://doi.org/10.31861/bmj2018.01.122

Chechetenko V. O. ¹ , Chuiko Oleksiy Serhiyovych ¹ , Chuiko Sergey Mykhailovych ²

¹ Donbass State Pedagogical University, Slaviansk, 84116, Ukraine

² Department of Mathematics and Informatics, Donbass State Pedagogical University, Slaviansk, 84116, Ukraine

DOI: https://doi.org/10.31861/bmj2018.01.122

Keywords: a nonlinear integral-differential boundary value problem, Newton-Kantorovich method, the conditions of convergence

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Abstract

Structural conditions for the existence of a nonlinear integral-differential boundary value problem are found. An iterative scheme with quadratic convergence is constructed to find the solution of a nonlinear integral differential boundary value problem based on the modification of the Newton-Kantorovich method. In order to justify the quadratic convergence of the modified Newton- Kantorovich method in the case of an undefined system, the original conditions of convergence are proposed.

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ACS Style: Chechetenko, V.O.; Chuiko, O.S.; Chuiko, S.M. The Newton-Kantorovich method in theory of nonlinear intergo-differential boundary value problem. Bukovinian Mathematical Journal. 2018, 6 https://doi.org/ https://doi.org/10.31861/bmj2018.01.122
AMA Style: Chechetenko VO, Chuiko OS, Chuiko SM. The Newton-Kantorovich method in theory of nonlinear intergo-differential boundary value problem. Bukovinian Mathematical Journal. 2018; 6(1-2). https://doi.org/ https://doi.org/10.31861/bmj2018.01.122
Chicago/Turabian Style: V. O. Chechetenko, Oleksiy Serhiyovych Chuiko, Sergey Mykhailovych Chuiko. 2018. "The Newton-Kantorovich method in theory of nonlinear intergo-differential boundary value problem". Bukovinian Mathematical Journal. 6 no. 1-2. https://doi.org/ https://doi.org/10.31861/bmj2018.01.122

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