Geodesic
On boundary value problems for singular systems of linear integro-differential equations method of least squares
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 2, pp. 81-94

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At present, in the analysis of complex electrical and electronic circuits, the system often includes interconnected differential, integral and algebraic equations. Algebraic equations are responsible for the difference of balance relations in the models, in particular, the conservation laws or equations of state, the system of differential equations describing the dynamics of the process. If the process has afteraction, the mathematical model can include integral equation (IE). The systems of interconnected differential, algebraic and integral equations can be written in the form of vector integro-differential equations with a matrix at the highest derivative of a searched vector-function of not full rank in the domain. Numerical solution of boundary and initial problems for such systems conjugates with great difficulty. In this paper we discuss the least squares method and the results of numerical calculations.
Keywords: degenerate system; general solution; integro-differential equations; boundary value problem; least squares method. 
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     title = {On boundary value problems for singular systems of linear integro-differential equations method of least squares},
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B. D. Nguyen; V. F. Chistyakov. On boundary value problems for singular systems of linear integro-differential equations method of least squares. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 2, pp. 81-94. http://geodesic.mathdoc.fr/item/VYURU_2015_8_2_a6/