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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2000 Volume 268, Pages 145–158 (Mi znsl1295)

This article is cited in 1 paper

The analytical (spectral) representation of the solution of delay algebraic-differential equations

V. B. Mikhailov

Center of Problems of Computer Aided Design of Institute for Computer Aided Design of RAS

Abstract: A new approach to finding analytical solutions of linear delay algebraic-differential equations is suggested. The analytical form of the solution is determined in terms of the infinite set of eigenvalues of a parametric matrix whose entries are the delay-time operators $\exp(-p\tau)$, where $p$ is the Laplace operator. In order to compute constants in the solution of the homogeneous equations, one must analytically find higher derivatives at the input of the delay operator. Issues of stopping the computation of the infinite spectrum upon determining a certain number of its components are discussed.

UDC: 517.518

Received: 01.09.2000


 English version:
Journal of Mathematical Sciences (New York), 2003, 114:6, 1836–1843

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