Various microband electrode problems are simulated using finite difference methods. These are (i) the chronoamperometric transient obtained under diffusion-only conditions, and (ii) the steady-state and (iii) the transient responses observed when the microband electrode is located in a convective flow. Three separate algorithms are employed to solve the problems, namely the strongly implicit procedure (STP), the alternating direction implicit (ADI) method and the backwards implicit (BI) method. The different approaches are compared and contrasted in terms of their relative efficiencies. Optimal simulation approaches to the solution of microband electrode problems are identified.