Two-dimensional digital simulation of chronopotentiometry at a microband electrode cannot be performed by conventional alternating direction implicit finite-difference simulation methods, as a result of non-local boundary conditions at the electrode. It is also potentially troublesome for iterative Krylov algorithms for solving linear algebraic equations that result from implicit temporal integration schemes. These difficulties can be avoided by representing the spatially discretised initial boundary value problem in the form of a set of differential-algebraic equations, to which a suitable integration scheme, such as the Rosenbrock ROWDA3 scheme, can be applied. The resulting linear algebraic equations can be solved unfailingly by a general direct sparse algorithm such as Y12M. Using this technique it has been found that the chronopotentiometric potential-time curves and transition time characteristics of a single charge transfer reaction at a microband electrode resemble those for a microhemicylinder electrode of the same surface area, although transition times are somewhat shorter. The simulation reveals also that the assumption of a uniform flux of the concentration at the electrode, encountered in the literature in the context of the two-dimensional theories of chronopotentiometry at microelectrodes, is not adequate, owing to non-negligible edge effects observed.