Splitting methods for differential approximations of the radiative transfer equation

The radiative transfer equation (RTE) has wide applications in sciences and engineering. Due to high dimensionality and integro-differential nature, the equation is difficult to solve numerically. In the literature, several approximation methods for solving the RTE numerically have been developed. Among them, a family of differential approximations of RTE, the so-called RT/DAE was proposed. In this paper, we establish a framework of the splitting method for RT/DAE and provide convergence analysis. We introduce the classic source iteration method, compare it with the new splitting method and prove the splitting method has superior convergence properties. Finally, we provide numerical examples demonstrating the effectiveness of the splitting method.