volume | PIER Journals

Abstract

The scattering problem from the random interface with the Dirichlet boundary condition can be formulated as an integral equation x = K̂y with respect to surface sources y (here, K̂ is the integral operator). Starting with an approximate operator K̂₀, for which the inverse operator M̂=K̂^âˆ’1₀ is known, the series in powers of the operator Ẑ=M̂(K̂₀âˆ’K̂) is derived. As an approximate kernel, we consider the kernel depending only on the difference of arguments: K₀=K₀(r-r´), for which the kernel of the operator M̂ can be found in terms of generalized functions. The norm of the difference operator ||Ẑ|| is found; the conditions of convergency ||Ẑ||≤ 1 were obtained.

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Professor V. Tatarskii