Finite difference methods convert ordinary differential equations (ODE) or partial differential equations (PDE), into a system of linear equations that can be solved by matrix algebra techniques
In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite volume. Because the flux entering a given volume is identical to that leaving the adjacent volume, these methods are conservative.