By using streamwise pressure gradient on the edge of the boundary layer instead of that in the boundary layer

traditional solution for streamwise pressure gradient in parabolized Navier-Stokes (PNS) equations was improved and applied to PNS equations as basic flows for stability analysis of hypersonic flows.Three typical examples with flat

blunt cone at zero and small angle of attack

were calculated.For the blunt three-dimension flows or two-dimension flows

PNS equations are reliable to get the hypersonic basic flows for stability analysis

and the results of the stability analysis are in good agreement with those obtained by solving Navier-Stokes (N-S) equations directly

but expense of time and space is an order of magnitude lower than N-S equations.