An optimization method based on a physical analysis of the temperature profile and different terms in the radiative transfer equation is developed to reduce the time computation of the net emission. This method has been applied for the cylindrical discharge in sodium vapor. Numerical results show a relative error of spectral flux density values lower than 5% with an exact solution, whereas the computation time is about 10 orders of magnitude less. This method is followed by a spectral method based on the rearrangement of the lines profile. Results are shown for Lorentzian profile and they demonstrated a relative error lower than 10% with the reference method and gain in computation time about 20 orders of magnitude.

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