A reliable modeling of spray combustion requires a detailed understanding of the physical and chemical processes, like vaporization, diffusion and chemical kinetics. A model for the ignition and combustion of a fuel spray is the combustion of an ensemble of single droplets. This system is suited to investigate the complex interplay of physical and chemical processes. Therefore, numerical simulations of single fuel droplets in a convective environment are performed to investigate the influence of ambient physical parameters, like gas temperature and gas flow velocity, on the ignition and combustion process. The transport processes, the phase transition and the chemical kinetics are modeled in detail. The conservation equations of the gas phase and the liquid phase are solved in a fully coupled way. Efficient numerical methods are applied to reduce the computing time. Nevertheless, the equation system is characterized by a large number of equations, and an extreme stiffness. This results in excessive computing times.