TITLE:
On the Telegrapher’s Equation with Three Space Variables in Non-Rectangular Coordinates
AUTHORS:
Tristan Guillaume
KEYWORDS:
Telegrapher’s Equation, Spherical Coordinates, Fourier-Bessel-Legendre Series Expansion, Associated Legendre Functions, Hyperbolic PDE, Initial Boundary Value Problem
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.5,
May
20,
2020
ABSTRACT: This article provides a closed form solution to the telegrapher’s equation with three space variables defined on a subset of a sphere within two radii, two azimuthal angles and one polar angle. The Dirichlet problem for general boundary conditions is solved in detail, on the basis of which Neumann and Robin conditions are easily handled. The solution to the simpler problem in cylindrical coordinates is also provided. Ways to efficiently implement the formulae are explained. Minor adjustments result in solutions to the wave equation and to the heat equation on the same domain as well, since the latter are particular cases of the more general telegrapher’s equation.