Main objective of this paper is to outline possibleways how to achieve a substantial acceleration in caseof advection-diffusion equation (A-DE) calculation,which is commonly used for a description of thepollutant behavior in atmosphere. A-DE is a kind ofpartial differential equation (PDE) and in general caseit is usually solved by numerical integration due to itshigh complexity. These types of calculations are timeconsuming thus the main idea of our work is to adoptCUDA platform and commodity GPU card to do thecalculations in a faster way. The solution is based onmethod of lines with 4th order Runge-Kutta scheme tohandle the integration. As a matter of fact, the selectedapproach involves number of auxiliary variables andthus the memory management is critical in order toachieve desired performance. We have implementedseveral possible solutions that use different memoryaccess schemes. Detailed evaluation is provided in thispaper where the obtained results show a tremendousprocessing speed up in comparison to CPU.