A second-order finite difference method for the resolution of a boundary value problem associated to a modified Poisson equation in spherical coordinates

We propose a second-order finite difference method which may be used for a self-contained and efficient numerical resolution of a boundary value problem involving a modified Poisson equation written in spherical coordinates and a Robin type boundary condition. We compare on two realistic examples issued from the combustion of a coal char particle the efficiency of this second-order finite difference method with that of the classical finite difference method and of the finite element method.