Self-consistent approximation: Development and application to the problem of waves in inhomogeneous media

A new self-consistent approximation proposed earlier, is compared with various existing approximations, as well as with a numerical simulation of solutions of the wave equation for a medium with one-dimensional inhomogeneities. The Green's function, found using the new approach, is the closest to the result obtained by the numerical simulation. The results of the work show that the new approach has undoubted advantages in the study of stochastic problems in media with longwave inhomogeneities. The new self-consistent approximation in some cases has advantages over a numerical method: a more rapid process of calculation and the possibility of consideration of three-dimensional problems. •Numerical solutions of the wave equation in the wide interval of correlation radius of inhomogeneities are carried out.•The solutions using the new SCA practically coincide with the results of numerical experiment.•The new SCA takes into account more diagrams then the well-known ladder approximation.