ИСТИНА

In this work, a quadrature formula for the double layer potential is derived in the case of the Helmholtz equation with continuous density given on a smooth closed or open surface. This quadrature formula gives higher computational accuracy than standard quadrature formula, which is confirmed by numerical tests. The advantage of the new quadrature formula is especially noticeable near the surface, where the standard quadrature formula diverges rapidly, while the new formula provides acceptable accuracy for points that are distant from the surface at distances comparable to the integration step and more.