The PNP system of equations is the standard model for characterizing the electrodiffusion of ions in electrolytes, including ionic dynamics in the cellular cytosol. This non-linear system presents challenges from both modeling and simulations due to the presence of a stiff boundary layer tightly related to the choice of boundary conditions. In this talk, I will present a scheme based on the DDFV method, to solve PNP while preserving the positivity of ionic concentrations. Using this scheme, I will then investigate the propagation and attenuation of ionic transients in dendritic neuronal compartments, such as synapses and bifurcations. Our results suggest that the local geometry of the dendritic tree has a major influence on synaptic functioning, giving a new paradigm to study neuronal plasticity, as synapses are usually considered as isolated compartments.