Method of iterated kernels in problem of wave propagation in heterogeneous media: calculation of higher orders terms

The approximated solution of wave propagation problem in smooth heterogeneous media by use of the iterated kernels method is proposed. It represents the result of iterated method application to the integral equation equivalent to the Helmholtz scalar equation. The resulting solution has a compact type and unites the advantages of the Born scattering and short-wave asymptotic methods. The way of increasing accuracy of the solution on the basis of addition of terms is shown. Their functional form is determined by the requirement of meeting the conditions of the Helmholtz equation solution and represents a compromise between the accuracy and the simplicity of the solution.