On Wavelet Based Modeling of the Nitrogen Oxides Emission and Concentration due to Road Traffic in Urban Environment

Abstract

Differential equations can be solved wavelet-based by representing the continuous functions by their wavelet expansion coefficients and thus the corresponding differential equations are transformed to matrix equations. The wavelet basis functions are organized into resolution levels of different frequency terms at different locations, and the main advantage of the wavelet expansion representation is that the wavelet based differential equation solving methods can be adaptive, it is possible to refine the solution locally, if the precision is not sufficient at some regions.

In case of the nitrogen oxides convection-advection equation, the urban environment should be taken as special material parameter in the differential equation's operator, and the matrix elements of the differential operator has to be calculated in a non-continuous environment, and the obstacles are placed so, that they are not at the boundaries of the support of the wavelets.