Geodesic
Multistep Method for Solving Degenerate Integral-Differential Equations
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 7 (2014) no. 3, pp. 93-106

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In this work we consider the linear integral-differential equations of the fist order with the identically singular matrix at the derivative. For these systems, the initial conditions is given and assumed consistent with the right part. Considered tasking in this paper arise in the mathematical modeling of complex electric circuits. By using the apparatus of matrix polynomials a class of problems, which having a unique solution, is marked out. The difficulties of the numerical solution of such problems, in particular the instability of many implicit methods is considered. For numerical solution of this class of problems we have suggested multistep methods, which are based on an explicit quadrature formula for the integral term Adams and extrapolation formulas. Sufficient conditions for the convergence of such algorithms to the exact solution is formulated.
Keywords: integral-differential equations; multistep methods; matrix polynomials. 
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     author = {M. V. Bulatov and Do Tien Thanh},
     title = {Multistep {Method} for {Solving} {Degenerate} {Integral-Differential} {Equations}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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M. V. Bulatov; Do Tien Thanh. Multistep Method for Solving Degenerate Integral-Differential Equations. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 7 (2014) no. 3, pp. 93-106. http://geodesic.mathdoc.fr/item/VYURU_2014_7_3_a9/