This thesis implements a new numerical scheme to solve the (classical) constant speed wave equation in the three dimensional space, currently existing methods (even if more restrictive) rely on time iterations and observe the accumulation of error at each time step iteration, the new method is iteration free ! Making it a good choice for applications requiring accurate results at large times. Numerical experiments and error analysis reveal accuracy of the scheme. The principal conclusion is that the method, based on the Radon transform, must be considered, and we propose it should be developed and count among the standard methods implemented in computational software for engineering and industrial applications.