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An application of a homotopy analysis method to nonlinear composites

In this paper, the homotopy analysis method is employed to decompose the classical boundary-value problem of nonlinear composite media into an infinite number of linear partial differential equations, solving each linear partial differential equation by separating variables together with the method of undetermined coefficients. Although the calculation is rather complicated, the solutions obtained in this paper have much higher precision than those known ones. We also investigate the effective conductivity of nonlinear composite media, and obtain an approximate expression for it.