Wedge diffraction is a well-known problem in applied mathematics. The currently favoured semi-analytical scheme is to reduce the original elastodynamic equations supplemented with boundary, radiation and tip conditions first to a system of functional equations and then to a system of algebraic and integral equations. The latter are to be solved numerically on a line in a complex plane; the solution is to be extended first to a strip centred on this line and then to the whole complex plane. We have investigated the latest contribution to the body of wedge literature provided by Budaev and Bogy, who followed Malyuzhinets and represented solutions of the elastodynamic equations using the Sommefeld integral transform. Our main achievement has been the clarification of the status of the unknown constants in the functional equations which emerge on substituting such transforms into boundary conditions, taking into account the tip conditions and applying the Nullification Theorem for the Sommerfeld Integrals. As the result we have developed a new numerical schedule for solution of the corresponding singular integral equations. This has now been implemented in a user-friendly code 2DWeC to compute Sommerfeld amplitudes which satisfy the functional equations, exhibit the correct behavior at infinity, possess correct singularities and do not possess parasitic singularities in the regions of interest. We argue that by implication the corresponding inverse transforms satisfy the original equations as well as boundary, radiation and tip conditions and thus constitute the solution of the original diffraction problem.
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