Math 228A - Numerical Solution of Differential Equations (Fall 2016)

Course details

Textbooks

Other resources

Grading

Schedule

Lec Date Topic Readings Other
1 W 8/24 Overview, ODEs (IVPs, BVPs), PDEs
2 F 8/26 IVP Theory L:5.1-5.2, Str:1-2, I:1.1,A.2.3
3 M 8/29 Basic Numerical Methods for IVPs L:5.3 , I:1.2,2.1,3.2
4 W 8/31 MATLAB, the ODE Suite ML, Mol, Sha
5 F 9/02 Convergence of Euler's Method Str:3.2, I:1.2
M 9/05 Labor day - No lecture
6 W 9/07 Stiff Equations L:8.1-8.2, Str:3.3, I:4.1-4.2
7 F 9/09 Linear Stability Theory, A-stability L:7.1-7.6, Str:3.5-3.6, I:4.2 PS1 Due
8 M 9/12 Implicit Methods Str:3.4, I:7.1-7.3
9 W 9/14 Taylor Series Methods L:5.6, Str:2.6
10 F 9/16 Explicit Runge-Kutta (ERK) Methods L:5.7, Str:4.1-4.4, I:3.2
11 M 9/19 Implicit Runge-Kutta (IRK) Methods I:3.3
12 W 9/21 Runge-Kutta Order Conditions Str:4.5, I:3.C
13 F 9/23 Gaussian Quadrature I:3.1 PS2 Due
14 M 9/26 IRK Methods from Collocation I:3.4
15 W 9/28 Lecture canceled
16 F 9/30 A-stability of Runge-Kutta Methods Str:4.6-4.8, I:4.3
17 M 10/03 L-stability and B-stability L:8.3, Str:4.9-4.10
18 W 10/05 Linear Multisteps Methods, Adams Methods L:5.9, Str:10.1-10.3, I:2.1
19 F 10/07 Backward Differentiation Formulae Methods L:8.4, Str:10.4, I:2.3 PS3 Due
20 M 10/10 Order and Convergence of Multistep Methods L:6.4, Str:11.1-11.5, I:2.2
21 W 10/12 A-stability of Multistep Methods L:7.3, Str:11.6, I:4.4
22 F 10/14 Stepsize and Error Control I:6.1-6.2
23 M 10/17 Embedded Runge-Kutta Methods Str:5.1-5.4, I:6.3
24 W 10/19 Finite Difference Approximations L:1.1-1.5, I:8.1
25 F 10/21 Convergence of BVPs L:2.1-2.10 PS4 Due
26 M 10/24 Boundary Layers and Nonuniform Grids L:2.12-2.17
27 W 10/26 FD methods for elliptic problems I L:3
28 F 10/28 FD methods for elliptic problems II L:3
29 M 10/31 FD methods for elliptic problems III L:3
30 W 11/02 FD methods for parabolic problems I L:9
31 F 11/04 FD methods for parabolic problems II L:9 [PS5 Due]
32 M 11/07 FD methods for parabolic problems III L:9
33 W 11/09 FD methods for hyperbolic problems I L:10
F 11/11 Veterans day - No lecture
34 M 11/14 FD methods for hyperbolic problems II L:10
35 W 11/16 FD methods for hyperbolic problems III L:10
36 F 11/18 Compact finite difference schemes I Lele92 [PS6 Due]
37 M 11/21 Compact finite difference schemes II Lele92
W 11/23 Thanksgiving - No lecture
F 11/25 Thanksgiving - No lecture
38 M 11/28 Spectral methods for BVPs I Tre
39 W 11/30 Spectral methods for BVPs II Tre
40 F 12/02 Spectral methods for BVPs III Tre [PS7 Due]
RRR week 12/5-12/9 - No lectures

MATLAB codes