We discuss preliminary calculations of impact‐parameter‐dependent probabilities and cross sections for muon‐pair production with capture of the negative muon into theK‐shell of the target caused by the time‐dependent electromagnetic fields generated in peripheral relativistic heavy‐ion collisions. Our approach is nonperturbative in that we calculate probabilities by solving the time‐dependent Dirac equation on a three‐dimensional Cartesian lattice using the basis‐spline collocation method. Use of the axial gauge for the electromagnetic potentials produces an interaction easier to implement on the lattice than the Lorentz gauge.