In this work we report the development of an implicit finite difference numerical method for the one space dimension time-fractional advection-diffusion equation, on a bounded domain, to model the transient electrical current of the time of flight experiment of disordered (e.g. organic) semiconductors. Some numerical experiments and simulation of experimental data are carried out showing that the presented model describes accurately the transient electrical current.
In this work we use tempered fractional advection-diffusion equations to model the dispersive transport in disordered materials. A numerical method is derived to approximate the solution of such differential models and we prove that it is convergent and stable. Two numerical examples are presented. The first one, with known analytical solution, is given to illustrate the performance of the numerical scheme; the second one is used to show that such models are appropriate to model time of flight transient currents for some disordered materials.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.