Solution of the one-dimensional transport equation by the vector Green function method: Error bounds and simulation

Abstract

In this work we solve the general anisotropic transport equation for an arbitrary source with semi-reflexive boundary conditions. First we present a complete existence theory for this problem in the space of continuous functions and in the space of α-Hölder continuous functions. As a result of our analysis we construct integral operators which we discretize in a finite dimensional functional space, yielding a new robust numerical method for the transport equation, which we call Green’s function decomposition method (GFD). As well, we demonstrate a convergence theorem providing error bounds for the reported method. Finally we provide numerical results and applications.