On the Telegrapher’s Equation with Three Space Variables in Non-Rectangular Coordinates

• 作者: Tristan Guillaume
• 来源期刊: 应用数学与应用物理(英文)
• 学科: 数学
• 关键词: Telegrapher’s EQUATION Spherical COORDINATES Fourier-Bessel-Legendre Series Expansion Associated LEGENDRE Functions HYPERBOLIC PDE Initial Boundary Value Problem
• 年，卷（期）: 2020,（5）
• 页码范围: 910-926
• 页数: 17页
• 分类号: O17

摘要

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.