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K. L. Cooke and D. W. Krumme, “Differential—Difference Equations and Nonlinear Initial Boundary Value Problems for Linear Hyperbolic Partial Differential Equations,” Journal of Mathematical Analysis and Applications, Vol. 24, No. 2, 1968, pp. 372-387. doi:10.1016/0022-247X(68)90038-3

has been cited by the following article:

• TITLE: Distortionless Lossy Transmission Lines Terminated by in Series Connected RCL-Loads

  AUTHORS: Vasil G. Angelov, Marin Hristov

  KEYWORDS: Lossy Transmission Line, RCL-Nonlinear Loads, Fixed Point, Periodic Solution

  JOURNAL NAME: Circuits and Systems, Vol.2 No.4, October 24, 2011

  ABSTRACT: The paper deals with a lossy transmission line terminated at both ends by non-linear RCL elements. The mixed problem for the hyperbolic system, describing the transmission line, to an initial value problem for a neutral equation is reduced. Sufficient conditions for the existence and uniqueness of periodic regimes are formulated. The proof is based on the finding out of suitable operator whose fixed point is a periodic solution of the neutral equation. The method has a good rate of convergence of the successive approximations even for high frequencies.