Description of the teaching content

Content (18h CM, 8h TD):

• Numerical resolution of linear systems of equations: direct methods (LU, Cholesky), iterative methods (Jacobi, Gauss-Seidel, relaxation, Krylov spaces, conjugate gradient). Sparse matrices.
• Numerical resolution of non-linear systems of equations : Picard’s iterations, Newton and quasi Newton methods.
• Numerical resolution of differential equations. One-step methods (Runge-Kutta). Multi-step methods. Stability notions.
• Stiff problems, implicit methods.
• Programming langage : Octave/Matlab

Skills to be acquired

Objectives:

• Being able to write a simple program.
• Being able to solve a system of linear equation.

Skills to acquire:

• choose the numerical resolution technique best suited to solve a given engineering problem.
• know how to use numerical techniques.
• understand how numerical tools work.