Advanced Numerical Methods
- An introduction to numerical methods- error analysis
- Non-linear algebraic equations methods (general eq.)
- Non-linear algebraic equations methods (polynomial eq.)
- System of linear and nonlinear equations plus eigenvalue problems direct and iterative methods
- Interpolation and extrapolation methods (Spline – Bezier – B-spline - Least squares)
- Interpolation and extrapolation polynomials (Newtonian and Lagrangian)
- Numerical integration and differentiation first and higher order estimates
- Numerical integration using approximate functions + composite integration formulas
- Numerical integration using Gaussian quadratures
- Numerical solutions for ordinary differential equations (IVP) single and multi-step methods
- Numerical solutions for ordinary differential equations (BVP) shooting method and finite difference
- Numerical solutions for partial differential equations (elliptic eq.)
- Numerical solutions for partial differential equations (parabolic eq.)
- Numerical solutions for partial differential equations (hyperbolic)
- Other solution methods for PDEs in literature (FEM - DQ - GDQ - EKM - ....)
- Introduction to finite element method