The evolution of linearized perturbations in a magnetohydrodynamic shear flow is studied using the initial value problem approach. Here the resulting equation in time posed by using the Fourier transform is solved for the Fourier amplitudes for modeled boundary layer for different initial disturbances. The shear flow prototype here is a piecewise linear approximation of a magnetohydrodynamic boundary layer. The initial disturbances that are considered are a point source of the field of transverse velocity and magnetic field. Solutions are obtained for small values of Alfve’n velocity. The velocity plots are drawn for different values of Alfve’n velocity.