We consider numerical simulation of temporal hydrodynamic instability with finite amplitude perturbations in plane incompressible Poiseuille flow. Two dimensional Navier Stokes equations have been used and reduced to vorticity-stream function form. Trigonometric polynomials have been used in homogeneous direction and Chebyshev polynomials in inhomogeneous direction. The problem of boundary conditions for vorticity has been solved by using the method of influence matrices. The Orr-Sommerfeld equation has been solved by Chebyshev polynomials, and linear combination of the obtained eigenfunctions has been optimized with regard to the corresponding eigenvalue. We present here the results of simulation for the perturbations optimized in regard to the least stable eigenvalue for the Reynolds number Re =1000.