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Non-local telegrapher’s equation as a transmission line model

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  • Cvetićanin, Stevan M.
  • Zorica, Dušan
  • Rapaić, Milan R.

Abstract

Transmission line displaying non-locality effects is modelled by considering the magnetic coupling of inductors in the series branch of Heaviside’s elementary circuit, so that the magnetic flux is obtained as a superposition of local and constitutively given non-local magnetic flux through the cross-inductivity kernel. Non-local telegrapher’s equations are derived as the continuum limit of corresponding Kirchhoff’s laws and solved for prescribed external excitation analytically by the means of integral transforms method and also numerically. Numerical examples of the mollified impulse responses illustrate the non-local behavior of signal propagation in case of power, exponential, and Gauss type cross-inductivity kernels.

Suggested Citation

  • Cvetićanin, Stevan M. & Zorica, Dušan & Rapaić, Milan R., 2021. "Non-local telegrapher’s equation as a transmission line model," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    • Handle: RePEc:eee:apmaco:v:390:y:2021:i:c:s0096300320305579
    DOI: 10.1016/j.amc.2020.125602
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    References listed on IDEAS

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    1. Weiss, George H, 2002. "Some applications of persistent random walks and the telegrapher's equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 381-410.
    2. J. Quintana-Murillo & S. B. Yuste, 2011. "An Explicit Numerical Method for the Fractional Cable Equation," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-12, September.
    3. Vitali, Silvia & Castellani, Gastone & Mainardi, Francesco, 2017. "Time fractional cable equation and applications in neurophysiology," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 467-472.
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