 
Summary: Journal of Computational Physics 162, 536543 (2000)
doi:10.1006/jcph.2000.6547, available online at http://www.idealibrary.com on
NOTE
An Integral Evolution Formula for the
Wave Equation
Bradley Alpert,,1
Leslie Greengard,,2
and Thomas Hagstrom,3
National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80303,Courant Institute
of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 100121110, and
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131
Email: alpert@boulder.nist.gov, greengar@cims.nyu.edu, hagstrom@math.unm.edu
Received September 10, 1999; revised April 6, 2000
We present a new timesymmetric evolution formula for the scalar wave equation.
It is simply related to the classical D'Alembert or spherical means representations,
but applies equally well in two space dimensions. It can be used to develop stable,
robust numerical schemes on irregular meshes. c 2000 Academic Press
Key Words: smallcell problem; stability.
1. INTRODUCTION
It is notoriously difficult to construct stable highorder explicit marching schemes for
