Numeric solution of systems of nonlinear Volterra integral equations of the first kind with discontinuous kernels

The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified Newton-Kantorovich iterative process for the integral operators linearizatio...

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Bibliographic Details
Published inarXiv.org
Main Authors Tynda, A N, Sidorov, D N, Sidorov, N A
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.10.2019
Subjects
Discontinuity
Integral equations
Iterative methods
Kernels
Mathematical analysis
Nonlinear equations
Nonlinear systems
Numerical analysis
Numerical methods
Operators (mathematics)
Polynomials
Volterra integral equations
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Summary:The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified Newton-Kantorovich iterative process for the integral operators linearization. On each step of the iterative process the linear system of integral equations is obtained and resolved using the discontinuity driven piecewise constant approximation of the exact solution. The convergence theorem is proved. The polynomial collocation technique is also applied to solve such systems as the alternative method. The accuracy of proposed numerical methods is discussed. The model examples are examined in order to demonstrate the efficiency of proposed numerical methods and illustrate the constructed theory.
ISSN:2331-8422