Geodesic
Solvability and numerical solutions of systems of nonlinear Volterra integral equations of the first kind with piecewise continuous kernels
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 1, pp. 130-136 Cet article a éte moissonné depuis la source Math-Net.Ru

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The existence theorem for systems of nonlinear Volterra integral equations kernels of the first kind with piecewise continuous is proved. Such equations model evolving dynamical systems. A numerical method for solving nonlinear Volterra integral equations of the first kind with piecewise continuous kernels is proposed using midpoint quadrature rule. Also numerical method for solution of systems of linear Volterra equations of the first kind is described. The examples demonstrate efficiency of proposed algorithms. The accuracy of proposed numerical methods is $\mathcal{O}(N^{-1})$.
Keywords: Volterra integral equations; discontinuous kernel; ill-posed problem; evolving dynamical systems; quadrature; Dekker–Brent method. 
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     title = {Solvability and numerical solutions of systems of nonlinear {Volterra} integral equations of the first kind with piecewise continuous kernels},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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     language = {en},
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I. R. Muftahov; D. N. Sidorov. Solvability and numerical solutions of systems of nonlinear Volterra integral equations of the first kind with piecewise continuous kernels. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 1, pp. 130-136. http://geodesic.mathdoc.fr/item/VYURU_2016_9_1_a10/

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