A two-fluid hydrodynamic model of a two-dimensional gas-solids fluidized bed is used to calculate the shape of an isolated bubble. The calculations are done by applying four different discretization schemes to the convection term. The bubble shape calculated by using the first-order upwind (FOW) scheme is unphysical and pointed, where as the bubble shape calculated by the second-order schemes SMART, Superbee, and MINMOD is physically realistic and rounded. Grid independence of the solutions is established. Superbee and SMART are found to give the most accurate results for a given grid resolution. Higher order discretization schemes are implemented with a downwind factor (DWF) method and with a deferred correction (DC) method. The DC method is significantly faster than the DWF method.