Lecturer: Weizhu Bao
http://www.math.nus.edu.sg/~bao/teach/ma5233/ma5233.html
Detailed Course Outline
- Introduction (lectures 1-2)
- History and milestone algorithms lecture 1
- Basic concepts:
- Numerical error
- Convergence and order of accuracy
- Stability and conditioning number
- Basic techniques lecture 2
- Asymptotic error expansion
- Richardson extrapolation
- Perturbation analysis
- Some techniques to reduce round-off errors
- Iterative methods for linear systems (lectures 3-4)
- Introduction lecture 3
- Classic iterative methods
- Jacobi Method
- Gauss-Seidel method
- Successive Overrelaxation method (SOR)
- Convergence analysis
- Krylov subspace methods lecture 4
- Steepest descent method
- Conjugate gradient (CG) method
- Preconditioning
- GMRES for nonsymmetric matrix
- Methods for nonlinear systems (lecture 5)
- Introduction lecture 5
- Newton’s method
- Quasi-Newton method
- Convergence analysis
- Numerical methods for ODEs (lectures 6-8)
- Introduction lecture 6
- Single-step method
- Euler methods
- Runge-Kutta methods
- Stability and convergence analysis
- Multi-step methods lecture 7
- Extension to first order systems and high order equations lecture 8
- Methods for stiff systems
- Numerical methods for PDEs (lectures 9-12)
- Introduction lecture 9
- Finite difference method
- Fast direct Poisson solvers lecture 10
- Convergence analysis
- Methods for time-dependent problems lecture 11
- Finite element method lecture 12
- Multigrid method
My notes: Runge-Kutta Methods, Multi-step Methods
Ngô Quốc Anh 