Approximate Solution to the Problem of Wave Diffraction by an Inhomogeneous Sphere.

A solution to the problem of diffraction of a plane harmonic wave by an inhomogeneous sphere is constructed in a long-wave approximation. The second-order equation with variable coefficients obtained after separation of variables is solved by a method based on approximating the solutions of ordinary differential equations by polynomials. A theorem concerning the existence and uniqueness of the solution of this equation is formulated and proven. The problem posed is thus reduced to the solution of a system of linear algebraic equations.