Modelling of some electrochemical reactions leads to systems combining ordinary differential equations (ODE) and partial differential equations (PDE). Using the Laplace transform method, the mass-transfer equations can be solved for thin-layer materials to give theoretical expressions for the related transfer functions containing terms such as tanh root taus / root taus or coth root taus / root taus or a combination of these terms, depending on the mass-transfer boundary conditions. Using transfer functions makes it possible to transform the PDEs into systems of ODEs of infinite size which can be solved numerically after truncation. This method is used here to study electrochemical insertion reactions in thin films of host materials by linear sweep voltammetry (LSV).