Course Syllabus 2014/2015
 
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Module : AN100
Title :
Numerical Analysis part I
Number of hours :
Lecture : 20.00 h
Tutorial classes : 24.00 h
Individual work : 22.00 h
ECTS credits :
5.00
Evaluation :
Teacher(s) :
DOBRZYNSKI CÚcile
SANTUGINI Kevin
TURPAUT Rodolphe - Responsible
Shared by UV(s) :
Level :
first year module
Abstract :
The goal of this lecture is to introduce the basic methods of numerical analysis. This introduction covers all the aspects of the methods from the mathematical analysis to the practical aspects. Topics include interpolation, quadrature and numerical methods for ODE. Links to applications are given.
Plan :
1 - Interpolation Lagrange and Hermite polynomials, divided differences. Interpolation residual, Runge phenomenon.

2 - Quadrature General definitions. Classical methods: rectangles, trapezoidal rule, Simpson's method. Newton-Cotes methods. Gauss methods: Gauss-Legendre, Gauss-Lobatto. Other scalar products: Gauss-Laguerre, Gauss-Chebyshev...

3 - Numerical methods for ODEs. Classical one-step methods: Euler, Runge, Heun. Runge-Kutta methods: formalism, Butcher tableau, order conditions, A-stability. Multistep methods: Adams, BDF and predictor-corrector methods, order conditions, 0-stability, convergence, A-stability.