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Lecture Notes

MATLAB® software is required to run the .m files in this section.

The lecture notes are available as a single (PDF) file, or as separate files related to the lectures in the table below.


LEC # TOPICS NUMERICAL EXAMPLES AND HANDOUTS
1 Introduction, Examples
2 Linear Systems
3 The Fast Fourier Transform (PDF)
4 Wave Equation (PDF) Supplemental Handout (PDF)
5 Consistency, Stability, Convergence, Von Neumann Analysis (PDF)
6 Conditions for Stability (PDF)
7 Multistep Schemes

Leap-frog (PDF)
8 Dissipation (PDF) Numerical Example (M)
9 Dispersion (PDF)
10 Group Velocity and Propagation of Wave Packets I (PDF) Numerical Example (M)
11 Group Velocity and Propagation of Wave Packets II (PDF)
12 Parabolic Equations (PDF) Supplemental Handout (PDF)
13 The Du Fort Frankel Scheme (PDF) Numerical Example (M)
14 The Convection-Diffusion Equation (PDF) Numerical Example (M)
15 Systems of Differential Equations (PDF)
16 The Solution of the System ut + Aux = Bu (PDF)
17 The Solution of the System ut + Aux = Buy (PDF)
18 ADI Methods (PDF)
19 Elliptic Equation (PDF)
20 Numerical Methods for Elliptic Equations (PDF)
21 Detailed Analysis of Jacobi, Gauss-Seidel and SOR(w) (PDF)
22 Multigrid, Part I Numerical Example Mgdemo.m and others located here
23 Multigrid, Part II
24 Numerical Methods for ODEs (PDF) Numerical Example (M)
25 Stiff ODEs (PDF)