Integration Formulas for the Wave Equation in n Space Dimensions
Abstract
We consider the wave equation in n space dimensions ( {∂ ^{2}u }/{∂t ^{2}})  ( {∂ ^{2}u }/{∂x _{1}^{2}})  …  ( {∂ ^{2}u }/{∂x _{n}^{2}}) = F(x _{1},…,x _{n},t) We derive formulas to approximate u at a point ( x_{01},…, x_{0 n}, t_{0}) assuming u( x_{1},…, x_{n}, 0) = f( x_{1},…, x_{n}) and u_{t}( x_{1},…, x_{n}, 0) = g( x_{1},…, x_{n}) are given. The formulas are exact when f, g, and F are arbitrary polynomials of degree ⩽ d, for various integers d, and are approximations to integrals which represent the solution.
 Publication:

Journal of Computational Physics
 Pub Date:
 September 1977
 DOI:
 10.1016/00219991(77)900249
 Bibcode:
 1977JCoPh..25...32S