Syllabus
* Numerical solution of Linear systems
- Direct methods - Gauss elimination. LU decomposition
- Iterative methods - -Jacobi, Gauss-Seidel methods, relaxation methods, conjugate gradient method. GMRES
* Nonlinear equations and systems of nonlinear equations.
* Approximation and interpolation
- Least square method
- Lagrange and Newton interpolations, spline functions.
* Numerical integration: Newton-Cotes formulas, Riachardson
- extrapolation, Romberg integration.
* Numerical solution of ODR - Cauchy problem
- Basic concept - approximation, stability, convergence, truncation error, global error.
- One-step methods - Runge-Kutta methods, method based on Taylor series
Annotation
The course, together with the Methods of Numerical Mathematics II, covers fundamentals of the numerical mathematics. The course is devoted to mathematical modelling and numerical solution of the ordinary and partial differential equations.