Dr. Dragan Jakimovski, Professor
Dr. Vlado Spiridonov, Professor
Course content:
Partial differential equations, boundary and initial conditions
Orthogonal functions and Fourier analysis (series, integrals, transforms)
One-dimensional problems (diffusion, advection), discretization, solution schemes, semi-Lagrangian method
Two-dimensional and multi-dimensional problems, differences and challenges
Numerical solution of partial differential equations, finite difference method
Time differentiation schemes
Two-level time schemes (Eulerian, backward scheme and trapezoidal scheme) Iterative schemes (Matsun and Hyun scheme) Introduction to python programming in a unix (linux) environment
Approximations in integration, approximations of functions on a sphere
Discretization and convergence errors
Nonlinear instability, filtering, spectral methods
Numerical stability
Modeling of randomness, probability, distributions
Random processes and time series
Numerical analysis of time series
Fourier analysis (periodogram), autocorrelation
Deterministic and stochastic dynamical systems
Neural networks in modeling atmospheric processes
Data assimilation and their statistical processing, correlation, regression
Reliability of numerically obtained results and degree of reliability of forecast
Extreme events