Teaching

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
Email 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