Year 2022-2023

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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

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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

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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

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Tools

• For the first part: Python.

• For the second part: DynIbex and c++.

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