Combined numerical method for solving of one degenerate integro-differential delay equation

Abstract

We have developed a numerical method for solving nonlinear degenerated integro-differential equation with delay, which appears when transients in radio technical systems are described. The matrix coefficient of derivative may be non-invertible. To discretize this equation, the method of Rietz type spectral projectors, explicit Euler scheme and left rectangles quadrature are used. The difference equation obtained during discretization is solved using simple iteration method. Convergence of developed numerical method is proved as a theorem.