Numerical simulation results for the spectral density of noise due to current fluctuations are presented. The mathematical framework is based on the interpretation of the equations describing electron transport in the semiclassical transport model as stochastic differential equations (SDE). Within this framework, it was previously shown that the autocovariance function of current fluctuations can be obtained from the transient solution of the Boltzmann transport equation (BTE) with special initial conditions. The key aspect which differentiates this approach from other noise models is that this approach directly connects noise characteristics with the physics of scattering in the semiclassical transport model and makes no additional assumptions regarding the nature of noise. The solution of the BTE is based on the Legendre polynomial method. A numerical algorithm is presented for the solution of the transient BTE. Numerical results are in good agreement with Monte Carlo noise simulations for the spectral density of current fluctuations in bulk silicon.