An analytical solution for the general perturbative diffusion equation by integral transform techniques

In this work, we present analytical solutions for the eigenvalue problem of a neutron flux in a rectangular two dimensional geometry by a two step integral transform procedure. For a given effective multiplication factor Keff we consider a homogeneous problem for two energy groups, i.e. fast and thermal neutrons, respectively, where the problem is setup by two coupled bi-dimensional diffusion equations in agreement with general perturbation theory (GPT). These are solved in a two-fold way by integral transforms, in the sequence Laplace transform followed by GITT and vice versa. Although, the functional base and the employed integral transforms are the same for both sequences, the procedures differ. We verify the efficiency of the sequence on the solutions of such problems, further the results are compared to the solution obtained by the finite difference method.