Ngô Quốc Anh

November 18, 2008

MA5233 – Computational Mathematics

Filed under: Linh Tinh — Ngô Quốc Anh @ 19:25

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)

My notes: Runge-Kutta Methods, Multi-step Methods

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