Abstract <p>The three-dimensional exterior Neumann problem for the Helmholtz equation is considered. Using the potential method, we reduce it to a weakly singular boundary Fredholm integral equation of the second kind, which is solved numerically. To improve the accuracy of the numerical solution algorithm and to reduce its computational complexity, we average the kernel of the integral operator and localize its singular part during discretization by applying simple analytical expressions. Examples of using this approach in the numerical solution of the original problem are given.</p>