Text

Uri Ascher, Numerical Methods for Evolutionary Differential Equations , SIAM, 2008.
There is a copy of this book in the reading room, on the reserved course material shelf. An e-copy is available throught the UBC library.
Check also
Solutions/additional examples
and
Errata

Lecture ``slides''

• The following extended talk Surprising computations will be discussed in class. It can serve as an appetizer or ``teaser'' until then.
  If you understand it all upon browsing through then there is probably no reason to take the course.
• Chapter 1: introduction
• Chapter 2: methods and concepts for ODEs
• Chapter 3: finite differnce and finite volume PDE discretizations
• Chapter 4: stability for constant coefficient problems
• Chapter 5: variable coefficient and nonlinear problems
• Chapter 6: Geometric integration and symplectic methods
• Chapter 7: Dispersion
• Chapter 8: More on boundary conditions
• Chapter 9: several space variables and splitting
• Chapter 10 (mainly pictures): discontinuous solutions
• Chapter 16 Ascher-Greif, 2011

Assignments

• Assignment 1: due Thursday noon, September 20
• Assignment 1: solution
• Assignment 2: due Thursday noon, Oct. 4
• Assignment 2: solution
• Assignment 3: due Thursday noon, Oct. 25
  Please note typo in Question 4: the first time step should be .25 h^2, not .5h^2.
  Please email your programs for Questions 2 and 4 in one message with the subject "your name" Assignment 3 . Send it to cs520@cs.ubc.ca
• Assignment 3: solution
• Assignment 4: due Thursday noon, Nov. 8
• Assignment 4: solution

Midterm

Wednesday, October 17

Final project

There are two components in terms of deadlines:
• A short presentation (about 10 minutes) during the last week of November
• Final project (writeup) due: Friday, December 14. .
The combined project weight is 50%, so this should give you a rough idea of the intended scope: the actual work is basically like the four assignments combined.

Whatever you choose your project to be it should connect to the course material: ask yourself if you could do the project of your choice without any knowledge gained in the course, and if the answer is positive then select another project. Check with me if unsure.

Your project can be on anything you choose; say, something connected to your research direction! There are also lots of project topics that suggest themselves upon reading the text, extending some of the material that is mentioned but not exhausted there. Potential topics extending the text include:

• QuadTrees and OcTrees (Section 3.1)
• Geometric Integration other than symplectic methods (e.g. Lie group methods; Chapter 6)
• Spectral methods (Section 7.4)
• Boussinesq equations (Chapter 7)
• Nonlinear Schroedinger (Section 9.3)
• Inverse problems involving time dependent PDEs (Chapter 9)
• Additive methods; or exponential time differencing (Section 9.3)
• Particle methods (e.g. cloth example); perhaps Smooth particle hydrodynamics (SPH, Section 7.5)
• Semi-Lagrangian methods (Chapters 9 and 10)
• Shocks in more than 1D (Chapter 10)
• Any Chapter 11 topic

Web resources:

• You can access various on-line guides to MATLAB: see for instance the cpsc303 web page as well as Ian Mitchell's and Kevin Murphy's helpers.

Software

• CLAWPACK - A package for hyperbolic conservation laws written by R. LeVeque et. al.
• Toolbox of Level Set Methods - A package for level set methods, generally following Osher-Fedkiw, written by Ian Mitchell.

Demos