Syllabus
* Numerical solution of ODR - Cauchy problem
- Linear multi-step methods - Adams-Bashforth method. Adams-Moulton method, predictor-corector, stability, stiff equations.
* Numerical solution of ODR - boundary value problem
- Shooting method
- Finite difference approximation,stability, consistency, convergence.
- Variation formulation, Galerkin method.
* Partial differential equations
- Classification, Fourier analysis of linear PDE, characteristics, convergence, consistence, stability, FD methods, methods of lines, CFL condition, von Neumann analysis.
- Elliptic equations - discretisation, finite differences, five and nine-point scheme, boundary conditions, solving the linear system, accuracy and stability.
- Diffusion equation- finite differences, method of lines. Crank-Nicolson method. LOD and ADI method
- Advection equation - finite differences, methods of lines. Lax-Friedrichs. Lax-Wendroff. upwind methods. Beam-Warming. stability.
- Hyperbolic systems
Annotation
The course, together with the Methods of Numerical Mathematics I, covers fundamentals of the numerical mathematics. The course is devoted to mathematical modelling and numerical solution of the ordinary and partial differential equations.