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The modeling of atmospheric dispersion is the mathematical simulation of how pollutants are dispersed in the atmosphere. Based on the advection-diffusion equations describing the dispersion of pollutants, dispersal models are widely used to give a spatial variability of pollutants emitted mainly by agricultural activities and industrial facilities. In this context, an analytical model is presented to study the dispersion of pollutants in the atmospheric boundary layer. The solution procedure is based on dividing the planetary boundary layer into sub-domains, where in each sub-domain the eddy diffusivity and the wind speed take average values. The eddy diffusivity is expressed under unstable conditions and the wind speed is represented in its logarithmic form. The findings of the current study show that the developed model is successfully validated using data sets obtained from the Copenhagen diffusion experiments in unstable conditions, after this the model is numerically applied in order to observe, in a better way, the spread of the pollutant in the atmosphere.

In this paper we present a new formulation for the nonlinear Cauchy problem for elliptic equations. This formulation allows us to give a method for solving this class of problems. The nonlinear problem is reduced to a linear Cauchy problem for the Laplace equation coupled with a sequence of nonlinear scalar equations. We solve the linear problem using the iterative method introduced in [7]. The linear dense systems obtained from a boundary element approximation are solved using an efficient implementation which accelerate the iterative process. Various types of convergence, comparison results and effects of small perturbations on boundary data are investigated. The numerical results show that the method produces a stable good approximate solution.

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This paper presents a new algorithm for computing the transfer function from state equations for linear system, multi-input multi-output system (MIMO). This algorithm employs an approximation method, which uses Krylov subspace techniques for linear system. We have focused on the Lanczos-based using the properties of Schur complemnts. This approach reduces the computation of transfer function from state equation for linear system. Our discussion is supported by an assortment of numerical examples.