  In this study, we consider the numerical solution of the Neumann initial
boundary value problem for the wave equation in 2D domains. Employing the
Laguerre transform with respect to the temporal variable, we effectively
transform this problem into a series of Neumann elliptic problems. The
development of a fundamental sequence for these elliptic equations provides us
with the means to introduce modified double layer potentials. Consequently, we
are able to derive a sequence of boundary hypersingular integral equations as a
result of this transformation. To discretize the system of equations, we apply
the Maue transform and implement the Nystr\"om method with trigonometric
quadrature techniques. To demonstrate the practical utility of our approach, we
provide numerical examples.
