An analytical solution for the one-dimensional time-dependent SN transport equation for bounded and unbounded domains in cartesian geometry

In this work a general analytical solution is reported, expressed in integral form the time-dependent, one-dimensional SA transport equation in cartesian geometry valid for bounded and unbounded domains (0 <x < infinity), using the double Laplace transform technique. The main idea consists in the application of the Laplace transform technique in time variable and the solution of the resulting equation by the LTSN method using appropriate boundary conditions for bounded and unbounded domain problems. We also report about the numerical simulations carried out.