The parabolic fourth moment equation for a plane wave is integrated numerically using an adaptive grid algorithm . Results are compared with those from an accurate, but far less efficient, operator splitting method, and agree very closely . The adaptive approach has several advantages over current fixed grid methods . The primary one is that significant reductions in computer memory usage can be obtained without a concomitant increase in run time . It is also ideally suited for accurate integration of the fourth-moment equation for an extremely large range of values of both the scattering parameter, F, and the wave propagation distance .

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The fourth-moment equation for the cross-frequency correlation of intensity fluctuations of a plane wave propagating in a random medium is solved numerically by using an adaptive grid method. A wide range of frequency ratios r and scattering strength parameters Gamma are considered, and approximate laws for the height and position of the peak of the covariance of intensities are obtained as functions of r and Gamma. Difficulties arising in the analytical solution of the fourth-moment equation are discussed.