Comment on the use of Hadamard’s example in ’’Numerical spatial marching techniques in duct acoustics’’ [J. Acoust. Soc. Am. 65, 297–306 (1979)]

This note clears up some possible confusion concerning the numerical solution of an initial value problem for the Helmholtz equation. An example is given which demonstrates that the initial value problem for the Helmholtz equation is ill-posed in the sense that small errors in the initial data lead to large errors in the solution. A stable numerical marching technique for such an ill-posed problem is described as a regularized problem in the sense of Tikhonov.