Huk L. Method of explicit counting for solving convective diffusion equation for problems of dynamic meteorology.

The thesis is for a scientific degree of a candidate of physics and mathematics sciences in the speciality 01.05.02 - mathematical modeling and numerical analysis. - Kiyiv national Taras Shevchenko University, Kiyiv, 2010. The thesis deals with numerical methods of implementation of a mathematical model of general atmospheric circulation. Special attention is paid to the question of optimization of computing time needed for realization of the model. A new unconditionally stable finite-difference scheme for solving a one-dimensional convective diffusion problem is proposed in the thesis. The method is based on putting onto different time layers the on-stream and upstream differences used in approximation of the first and the second space derivatives. In this way an implicit scheme is counted step by step using a so called explicit counting. This approach provides a possibility to decrease the time needed for solving the dynamic meteorology problem, but at the same time not to lose in accuracy. The results of theoretical study and testing of the scheme prove its efficiency and expediency of its utilization for dynamic meteorology problem solving.