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
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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.
@article{VYURU_2016_9_1_a10,
author = {I. R. Muftahov and D. N. Sidorov},
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},
pages = {130--136},
publisher = {mathdoc},
volume = {9},
number = {1},
year = {2016},
language = {en},
url = {http://geodesic.mathdoc.fr/item/VYURU_2016_9_1_a10/}
}
TY - JOUR AU - I. R. Muftahov AU - D. N. Sidorov TI - Solvability and numerical solutions of systems of nonlinear Volterra integral equations of the first kind with piecewise continuous kernels JO - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie PY - 2016 SP - 130 EP - 136 VL - 9 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VYURU_2016_9_1_a10/ LA - en ID - VYURU_2016_9_1_a10 ER -
%0 Journal Article %A I. R. Muftahov %A D. N. Sidorov %T Solvability and numerical solutions of systems of nonlinear Volterra integral equations of the first kind with piecewise continuous kernels %J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie %D 2016 %P 130-136 %V 9 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/VYURU_2016_9_1_a10/ %G en %F VYURU_2016_9_1_a10
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/