Abstract: P3 approximation of raditive transfer equation in spherical coordinate results nonlinear differential equations.Their solution are spherical Bessel functions. Particular solutions are obtained with variation of parameters in exponenital representation of spherical Bessel functions.Approximation boundary condition of Marshak and others can not be satisfied due to solution discontinuity at r=0.It is solved by energy conservation with approximation of P3 by P1 as absorption coefficient is much lower than reduced scattering coefficient.Compared with Monte Carlo and analytic solutions of P3 approximation,it is found that P3 approximation deals with biological tissues with ratios of reduced scattering coefficient to absorption coefficient from 2 to 10.

Key words: radiative transfer equation, P3 approximation, method of variation of parameters, spherical Bessel function