TW764 (2018) Introduction to finite difference and finite element methods Stellenbosch University Applied Mathematics

Important notices:

• Short solutions to Assignments 1-3 can now be found below.
• The first test is scheduled for Monday, 17 September, 9:00 to 11:00. It covers all material from the finite difference part of the course. You have to be able to (a) use stability regions to derive step size restrictions for A-stability, (b) compute the local truncation error of a fully discrete scheme and decide whether it is consistent, (c) derive a CFL condition for a fully discrete method, (d) apply a von Neumann stability analysis, and (e) be able to apply the method of characteristics to linear and nonlinear first order PDEs. Successful application of (a)--(e) will earn you a passing mark. For a distinction a bit more will be required (the exercises recommended in the lecture notes would be a good place to start). You will not be expected to write nor interpret computer code.
• For supplementary reading, the book "Finite Difference Methods for Ordinary and Partial Differential Equations" by RJ Leveque has been put on reserve at the Engineering Library. Please consult it.
• There will be no lecture on Tuesday, 18 September.

MATLAB:

• The first half of the module assumes some previous computational experience (MATLAB or Python).
Class room demos will use MATLAB.
• MATLAB is now FREE for all SU students. Download instructions here.
Alternatively, you can use MATLAB in your browser, but this may be slower.
• We strongly recommend completing the (free) online MATLAB Onramp as a refresher. (Sign in with SU credentials.)

First term:
Second term:

Information Sheet:

• Information sheet can be found here.

Lecture timetable:

• Tuesday 12:00 in A409
• Thursday 10:00 in A409
• Thursday 11:00 in A409

Tutorials:

• None in first half.

Assignments:

Assignment Due date Solutions
Assign_01.pdf 2018/08/10 Assign_01_sols.pdf
Assign_02.pdf 2018/08/24 Assign_02_sols.pdf
Assign_03.pdf 2018/09/07 Assign_03_sols.pdf
Tut1.pdf 2018/09/28
Tut2.pdf 2018/10/05
Tut3.pdf 2018/10/12
Tut4.docx 2018/10/19
Tut5.pdf 2018/10/26

Lecture notes:

Lecture 4 (2018/07/31) Stability regions: derivation
Lecture 5 (2018/08/02) Stability regions: diagrams
Lecture 6 (2018/08/02) Eigenvalues of second derivative matrix: derivation; Instability in the heat equation: demo

Lecture 7 (2018/08/07) Intro to characteristics (linear, first order PDEs)
Lecture 8 (2018/08/09) Further discussion of characterstics. Self-study (but you can skip Sections 11.4 and 11.5)
Lecture 9 (2018/08/09) Ditto

Lecture 16 (2018/08/28) Fully discrete schemes: Von Neumann analysis (updated)
Lecture 17 (2018/08/30) Continuation of Lecture 16, no new notes
Lecture 18 (2018/08/30) Review exercise and case study: Lax-Wendroff method
FEM notes will be updated regularly: FEM notes