A high order approximation, the $SKN$ method—a mnemonic for synthetic kernel—is proposed for solving radiative transfer problems in participating medium. The method relies on approximating the integral transfer kernel by a sum of exponential kernels. The radiative integral equation is then reducible to a set of coupled second-order differential equations. The method is tested for one-dimensional plane-parallel participating medium. Three quadrature sets are proposed for the method, and the convergence of the method with the proposed sets is explored. The $SKN$ solutions are compared with the exact, $PN,$ and $SN$ solutions. The $SK1$ and $SK2$ approximations using quadrature Set-2 possess the capability of solving radiative transfer problems in optically thin systems.

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