Left: the ﹩{\rm{\nabla }}B﹩ drift velocity v_y for a magnetic field with a linear gradient. Results are shown for the Boris method, the guiding center approximation, and for the approximation of Equation (65). Right: relative difference in the ﹩{\rm{\nabla }}B﹩ drift velocity of the GCA compared to the Boris method. For this test case, ﹩\delta B/B\approx {v}_{0}﹩ (omitting SI units).