Qin Li, Fall 2017:
[Shi Jin, Fall 2016]:
Previous description:
Numerical Methods for Ordinary Differential Equations
- Basic ODE Theory
- Explicit and implicit methods, stability, Runge-Kutta and multistep methods, stiff problems
Finite Difference Methods for Elliptic Partial Differential Equations
- Iterative methods for solving large linear systems
Finite Difference Methods for Parabolic Partial Differential Equations
- Numerical differentiations
- Consistency, stability and convergence
- Multidimensional problems
Finite Difference Methods for Hyperbolic Partial Differential Equations
- Linear hyperbolic equations and their numerical discretizations
- Basic theory for nonlinear hyperbolic equations: shock formation, weak solution and entropy condition, Riemann problem
- Shock capturing methods: Godnov and Roe methods, high resolution methods (TVD and ENO), kinetic and relaxation methods
- Hamilton-Jacobi equations and the level set method for front propagation
Finite Volume Methods for Partial Differential Equations
Spectral Methods for Partial Differential Equations
- Fast Fourier transform
- Fourier spectral method, pseudospectral methods
semester:
Fall
prereqs:
an undergraduate course in PDEs (on the level of Haberman's book on ``Applied Partial Differential Equations'')
an undergraduate course in numerical analysis (on the level of Burden and Faires's book on ``Numerical Analysis'')
knowledge in a programming language (e.g., Fortran, C/C++, or Matlab)