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Integration of telegraph equations

Integration of telegraph equations ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 5, pp. 661–671.  c Pleiades Publishing, Inc., 2006. Original Russian Text  c Yu.S. Kolesov, A.S. Kirillov, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 5, pp. 620–629. PARTIAL DIFFERENTIAL EQUATIONS Yu. S. Kolesov and A. S. Kirillov Yaroslavl State University, Yaroslavl, Russia Received July 7, 2003 DOI: 10.1134/S0012266106050065 We consider a classical system of telegraph equations on an interval with boundary conditions at the endpoints; one of the boundary conditions is nonlinear. For this mixed boundary value problem, we develop a numerical integration algorithm that permits one to reveal subtle features of the solution dynamics in a relatively simple way. 1. STATEMENT OF THE PROBLEM The telegraph equations [1, pp. 173–192] ∂U ∂I ∂I ∂U = rI + L , = gU + C , (1) ∂x ∂t ∂x ∂t where U (t, x) is the voltage between the wires, I(t, x) is the current in the line, and r, L, g,and C are primary parameters of the line (r is the active resistance, g is the conductivity, L is the inductance, and C is the capacitance), play an important role in the description of the dynamics of http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Integration of telegraph equations

Kolesov, Yu.; Kirillov, A.
Differential Equations , Volume 42 (5) – Jun 15, 2006
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References (2)

Publisher
Springer Journals
Copyright
Copyright © 2006 by Pleiades Publishing, Inc.
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266106050065
Publisher site
See Article on Publisher Site

Abstract

ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 5, pp. 661–671.  c Pleiades Publishing, Inc., 2006. Original Russian Text  c Yu.S. Kolesov, A.S. Kirillov, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 5, pp. 620–629. PARTIAL DIFFERENTIAL EQUATIONS Yu. S. Kolesov and A. S. Kirillov Yaroslavl State University, Yaroslavl, Russia Received July 7, 2003 DOI: 10.1134/S0012266106050065 We consider a classical system of telegraph equations on an interval with boundary conditions at the endpoints; one of the boundary conditions is nonlinear. For this mixed boundary value problem, we develop a numerical integration algorithm that permits one to reveal subtle features of the solution dynamics in a relatively simple way. 1. STATEMENT OF THE PROBLEM The telegraph equations [1, pp. 173–192] ∂U ∂I ∂I ∂U = rI + L , = gU + C , (1) ∂x ∂t ∂x ∂t where U (t, x) is the voltage between the wires, I(t, x) is the current in the line, and r, L, g,and C are primary parameters of the line (r is the active resistance, g is the conductivity, L is the inductance, and C is the capacitance), play an important role in the description of the dynamics of

Journal

Differential Equations – Springer Journals

Published: Jun 15, 2006

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