Navarro, JaimeWarchall, Henry A.2018-08-222018-08-221995-06-15Navarro, J. & Warchall, H. A. (1995). Reflectionless boundary propagation formulas for partial wave solutions to the wave equation. <i>Electronic Journal of Differential Equations, 1995</i>(17), pp. 1-14.1072-6691https://hdl.handle.net/10877/7584We consider solutions to the wave equation in 3+1 spacetime dimen- sions whose data is compactly supported at some initial time. For points outside a ball containing the initial support, we develop an outgoing wave condition, and associated one-way propagation formula, for the partial waves in the spherical-harmonic decomposition of the solution. The prop- agation formula expresses the l-th partial wave at time t and radius a in terms of order-l radial derivatives of the partial wave at time t − ∆t and radius a − ∆t. The boundary propagation formula can be applied to any differential equation that is well-approximated by the wave equation outside a fixed ball.Text14 pages1 file (.pdf)enAttribution 4.0 InternationalOne-sided wave propagationWave equationReflectionless boundary conditionsPartial wavesSpherical-harmonic decompositionOpen-space boundary conditionsArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.