On the mixed initial Dirichlet - Neumann problem for the wave equation in the circle

The method of integral equation formulation, proposed by Eckhardt and El Sheikh, is extended to solve an even initial mixed problem for the first time. The truncation of the integral equation or, equivalently, the infinite homogeneous algebraic system to which the problem is converted, is justified. In addition, having carried out the progression of the procedures right to the numerical results at several cases, a clarified and comprehensive idea about the usefulness of the method is revealed.