Voigt lineshape function as a solution of the parabolic partial differential equation

The goal of this paper is to show that the Voigt function may be found as a solution of a parabolic partial differential equation, like the heat conduction equation or other diffusion equations. A square of the Gaussian half-width of the Voigt function plays the role of 'time' and initial conditions are determined by a Lorentz function. Some questions concerning the practical application of the numerical grid methods for the calculation of the Voigt function are discussed. It is shown, that in some cases the offered calculation algorithm can be both faster and more accurate than other known algorithms.