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The superconvergence of Multhopp's discretization for the solution to the normal wash integral equation for the flow past a curved plate is theoretically analyzed and numerically examined. It has been inferred that the Multhopp's discretization also has a superconvergence behavior in simulating the vortex sheet evolution. Further, an improved Multhopp's method is suggested and applied to the numerical simulation of a periodical evolution of a flat vortex sheet. To validate the results obained by the inviscid vortex method, the initial-value problem for the development of a shear layer at large Reynolds number is numerically investigated by solving the two-dimensional incompressible Navier-Stokes equations.