Professor: Bob Guy
UC Davis - Winter 2017
Course website: http://www.math.ucdavis.edu/~guy/teaching/228b/
This course is part of the sequence 228A-C on numerical methods for partial differential equations. The second quarter (228B) will focus on time dependent problems. The topics we will cover this quarter are listed below.
- Introduction (Fourier transforms, derivation of conservation laws, parabolic and hyperbolic PDEs)
- Numerical ODEs (briefly)
- Stability, accuracy, and convergence
- Von Neumann analysis
- Diffusion (reaction-diffusion) equation in multiple dimensions
- Nonrectangular geometry (logically quadrilateral grids and embedded grids)
- Methods for advection equation in 1D
- Dissipation and dispersion, modified equations
- Hyperbolic conservation laws
- Godunov method, wave propagation, and high-resolution methods