Year 2022-2023
Course objectives
1)Learn main algorithms to solve initial value problems for ordinary differential equations and differential algebraic equations;
2)Learn main algorithms to solve two point boundary value problems;
3)Learn main interval algorithms to solve initial value problems for ordinary differential equations with bounded uncertainties
This course is made of two parts:
- Classical numerical methods for various kinds of dynamical systems;
- Set-based methods to rugourously enclose solution of dynamical systems
Lecturer
- Julien Alexandre dit Sandretto, Associate professor U2IS
Lectures
Part 1 - lecture 1
Introduction on numerical simulation methods. In particular, a quick overview of the simulation engine of Simulink will be presented.
Slides Practical work:
Sheet
Part 1 - lecture 2
Single step methods to solve initial value problems for ODEs.
Slides Practical work:
Sheet (scripts)
Part 1 - lecture 3
Multi step methods to solve initial value problems for ODEs.
Slides Practical work:
Sheet (scripts)
Part 1 - lecture 4
Discontinuous initial value problems for ODEs and stability properties of numerical methods. Initial value problems for differential algebraic equations (DAEs).
Slides Practical work:
Sheet
Part 2 - lecture 1
Introduction to interval analysis.
Slides Practical work:
Sheet
Part 2 - lecture 2
Guaranteed numerical integration for initial value problems for ODEs.
Slides Practical work:
Sheet
Part 2 - lecture 3
Guaranteed numerical integration for initial value problems for DAEs.
Slides Practical work:
Sheet
Tools