This article is cited in 3 papers

On the solvability and numerical methods for solution of linear integro-algebraic equations

V. F. Chistyakov

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia

Abstract: We study solvability conditions for a system of Volterra equations with some identically degenerate or rectangular matrix at the main term. Connection is discussed of the solvability conditions and applicability of numerical methods for solving these systems. In particular, the conditions of the convergence of the least squares method with the error functional defined in Sobolev spaces are presented.

Keywords: integro-differential equation, index, least squares method, difference scheme, singular point.

UDC: 517.977

Received: 07.08.2012

 English version: Siberian Mathematical Journal, 2013, 54:4, 746–758

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