## MAT 425: Numerical Analysis II

## Spring 2017

Class Time | Tu,Th 10:30am – 11:45am |

Class Location | Tempe – WXLR A108 |

Instructor | Sébastien Motsch |

Office | WXLRA 836 |

smotsch@asu[dot]edu | |

Office Hours | Tu,Th 12:00pm – 1:00pm |

Class webpage | www.seb-motsch.com/teaching |

## Textbook

- Richard L. Burden, J. Douglas Faires, “Numerical Analysis” (9th edition)

### Course description

- 1) Basic concepts of numerical computations
- – numerical differentiation and integration

– algorithm implementation - 2) Initial value problems for ODE
- – Euler and Runge-Kutta method

– multistep method

– convergence, stability - 3) Boundary value problems for ODE
- – shooting methods

– finite difference methods - 4) Introduction to PDE
- – heat and wave equations

– finite difference method and CFL conditions

A **syllabus** is also available here.

**Mid-term:** it is scheduled for **Thursday March 2nd** in class, it will cover Basic concepts and Initial value problems for ODE.

**Project:** each group (2-3 students) will give a 30mn presentation (20-25mn presentation + 5-10mn of questions) in April.

### Class Schedule

Jan 10 – 12 | Presentation course-Review calculus (Taylor polynomial) |

Jan 17 – 19 | Bisection and Newton method, fixed-point iteration (2.1-2.3) |

Jan 24 – 26 | Numerical differentiation-integration (4.1-4.3) |

Jan 31 – Feb 02 | Review ODE (5.1) |

Feb 07 – 09 | Euler method, Runge-Kutta (5.2-5.4) |

Feb 14 – 16 | Error control, high-order ODE (5.5,5.9) |

Feb 21 – 23 | high-order ODE, stability (5.9-5.11) |

Feb 28 – Mar 02 | Review (solution), Mid-term |

Mar 7 – 9 | Spring-break |

Mar 14 – 16 | BVP (shooting method) (11.1,11.2) |

Mar 21 – 23 | BVP (Finite-Difference Method) (11.3-11.5) |

Mar 28 – 30 | Lab BVP (solution), Finite-Element Method (11.5) |

Apr 4 – 6 | Elliptic-Parabolic PDE (12.1-12.2) |

Apr 11 – 13 | Lab2 (solution), Parabolic PDE (12.2) |

Apr 18 – 20 | Hyperbolic PDE (12.3), Lab3 |

Apr 25 – 27 | Project |

### Class homework

Jan 19 | HW 1, solution |

Jan 26 | HW 2, solution |

Feb 02 | HW 3, solution |

Feb 09 | HW 4, solution |

Feb 16 | HW 5, solution |

Feb 23 | HW 6, solution |

Mar 23 | HW 7, solution |

Mar 30 | HW 8, solution |

Apr 6 | HW 9, solution |

Apr 13 | HW 10 |

Apr 20 | HW 11 |

Apr 27 | HW 12 |

### Idea for projects

**ODE systems**:

- Symplectic schemes
- Chaos behavior (ex. double pendulum, Lorenz attractor)
- Epidemic model (ex. SIR model)
- Neuron model (ex. FitzHugh–Nagumo model)

**PDE equations**:

- Traveling waves (Fisher-KPP eq.)
- Traffic flow model (ex. car traffic)
- Evacuation plan
- Infection spreading (ex. SIR model+diffusion )

### Extra

- Visualization of phase portraits
- Runge-Kutta RK4.m