Generalized characteristic functions for simultaneous linear differential equations with variable coefficients applied to propagation in inhomogeneous anisotropic media

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Abstract
A wide class of physical problems can be reduced to sets of simultaneous linear differential equations with variable coefficients. For critical coupling regions of the independent variable where the characteristic values of the coefficient matrix tend to merge, the standard technique employing similarity transformations does not convert the original set of differential equations into a form that is suitable for numerical computations. For these critical coupling regions we employ a nonsingular transformation matrix associated with variable characteristic values to convert the original equation to a form that can be more readily resolved analytically (using an iterative approach) or numerically. The method developed is applied to problems of radio wave propagation in inhomogeneous, anisotropic, dissipative media with critical coupling regions.

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