**Description**: Theory and practical methods for numerical solution of differential equations. Ordinary differential equations: Runge-Kutta and multistep methods, stability theory, stiff equations, boundary value problems. Partial differential equations: Finite difference and spectral methods for elliptic, parabolic and hyperbolic equations, stability, accuracy and convergence, von Neumann analysis and CFL conditions.**Prerequisites**: Math 128A or equivalent knowledge of undergraduate numerical analysis, MATLAB or equivalent programming experience.**Lectures**: MWF 10am - 11am, room 247 Cory.**Lecturer**: Per-Olof Persson, persson@berkeley.edu, 1089 Evans, Phone (510) 642-6947.

Office hours: Mon 12:30pm - 2pm and Fri 11am - 12:30pm in 1089 Evans.**GSI**: Noble Macfarlane, ntmacfarlane@berkeley.edu, 1044 Evans.

Office hours: Thu 9am - 11am in 1044 Evans.

**Required**:**[L]**R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems, SIAM 2007.

**Optional**:**[HWN1]**E. Hairer, G. Wanner and S. P. Norsett, Solving ordinary differential equations I, Springer 1993.**[HW2]**E. Hairer and G. Wanner, Solving ordinary differential equations II, Springer 2010.**[I]**A. Iserles, A First Course in the Numerical Analysis of Differential Equations, Second Edition, Cambridge University Press 2008.**[Tre]**L. N. Trefethen, Spectral Methods in MATLAB, SIAM 2000.

**Lecture slides**(*Note*: These might be frequently updated)- Ordinary differential equations (Full page, 6 per page)

**Various other study material****[Str]**J. Strain, Lecture notes Math 228A Fall 2008 (PDF1, PDF2, PDF3, PDF4, PDF5, PDF10, PDF11)**[ML]**The MATLAB Online Documentation.**[Mol]**C. Moler, Numerical Computing with MATLAB, SIAM 2004.**[Sha]**L. Shampine, M. Reichelt, The MATLAB ODE Suite, SIAM J. Sci. Comput. 1997.**[Bar]**Barrett et al, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM 1994.

Instructions for setting up a UC Berkeley Library Proxy Server for off-campus access to online books

UC Berkeley provides MATLAB licenses to students, see the UC Berkeley Software Central for details

Grades will be based entirely on the 7 problem sets. Please start early, it might be hard to get help the last few days before the due dates. Problem sets can be handwritten or typed, but must be clear and well organized. They can be handed in during the lecture on the due date or submitted online through bCourses. Computer codes should be submitted online, according to the instructions in each problem set.

It is encouraged to discuss the problem sets with other current students, but each student must write his/her own solutions and computer codes, and understand all the details of them. It is not permitted to consult any solutions from courses given in previous years (including both reference solutions and other students' problem sets).

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 |
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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 |
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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 |
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F 11/25 | Thanksgiving - No lecture |
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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 |

**Lecture 4**: rk4.m, ball1.m, ballanim.m**MATLAB C-mex template**: mextemplate.cpp**Lecture 6**: ball2s.m, conv1d.m, heat1d.m**Lecture 7**: stab_region_demo.m, lmmraseval.m**Problem Set 2**: pendplot.m**Lecture 8**: pendulum_impl.m**Lecture 13**: gaussquad.m, gaussquad_roots.m**Problem Set 3**: struct_data.mat, struct_plot.m**Problem Set 4**: heat2d_data.mat, heat2d_plot.m**Lecture 21**: lmmrasdemo.m**Lecture 22**: stepsize_control_demo1.m, stepsize_control_demo2.m**Lecture 23**: embedded_rk_demo.m