A numerical study is presented of reaction–diffusion problems having singular reaction source terms, singular in the sense that within the spatial domain the source is defined by a Dirac delta function expression on a lower dimensional surface. A consequence is that solutions will be continuous, but not continuously differentiable. This lack of smoothness and the lower dimensional surface form an obstacle for numerical discretization, including amongst others order reduction. In this paper the standard finite volume approach is studied for which reduction from order two to order one occurs. A local grid refinement technique is discussed which overcomes the reduction.
Reaction–diffusion equations, Singular source terms, Finite volume methods
Energy (theme 4)
Journal of Computational and Applied Mathematics
Simulation of developmental regulatory networks
Available online
Computational Dynamics

Ashyraliyev, M, Blom, J.G, & Verwer, J.G. (2008). On the numerical solution of diffusion-reaction equations with singular source terms. Journal of Computational and Applied Mathematics, 216(1), 20–38.