Numerical Solution for a Wave Equation Arising in Oscillations of Overhead Transmission Lines

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Year:
2016
Type of Publication:
Article
Keywords:
Wave Equation, Boundary Damping, Characteristics Curves, Richardson Extrapolation
Authors:
Bendise Huti; Lulezim Hanelli
Journal:
IJISM
Volume:
4
Number:
2
Pages:
91-97
Month:
March
ISSN:
2347-9051
Abstract:
Numerical solution is developed for a wave equation with boundary damping arising in the study of the physical phenomena of the oscillations that occur in overhead power transmission lines. The physical model is that of a string which is fixed at one end and the other end is attached to a dashpot system, where the damping generated by the dashpot is small. The mathematical model is an initial-boundary value problem for a weekly nonlinear hyperbolic differential equation with non-classical boundary conditions. The method of the characteristics in combination with Richardson extrapolation will be used to solve the problem. The numerical method proposed takes advantage of the special mesh generated by the characteristic curves of the equations to be solved and the specialty of the initial-boundary conditions involved. Numerical results are presented in this paper.

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