Geodesic
Numerical Solution of Volterra Integral Equations of the First Kind with Piecewise Continuous Kernel
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 7 (2014) no. 3, pp. 107-115

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Integral equations are in the core of many mathematical models in physics, economics and ecology. Volterra integral equations of the first kind with jump discontinuous kernels play important role in such models and they are considered in this article. Regularization method and sufficient conditions are derived for existence and uniqueness of the solution of such integral equations. An efficient numerical method based on the mid-rectangular quadrature rule is proposed for these equations with jump discontinuous kernels. The accuracy of proposed numerical method is $\mathcal{O}(N^{-1})$. The model examples demonstrate efficiency of proposed method: errors, two mesh differences and orders of convergent.
Keywords: Volterra integral equations of the 1st kind; evolving systems; Glushkov integral model; numerical method. 
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     author = {D. N. Sidorov and A. N. Tynda and I. R. Muftahov},
     title = {Numerical {Solution} of {Volterra} {Integral} {Equations} of the {First} {Kind} with {Piecewise} {Continuous} {Kernel}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {107--115},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2014_7_3_a10/}
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D. N. Sidorov; A. N. Tynda; I. R. Muftahov. Numerical Solution of Volterra Integral Equations of the First Kind with Piecewise Continuous Kernel. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 7 (2014) no. 3, pp. 107-115. http://geodesic.mathdoc.fr/item/VYURU_2014_7_3_a10/