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:

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## Part 1 - lecture 2

Single step methods to solve initial value problems for ODEs.

Slides Practical work:

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## Part 1 - lecture 3

Multi step methods to solve initial value problems for ODEs.

Slides Practical work:

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## 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:

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## Part 2 - lecture 1

Introduction to interval analysis.

Slides Practical work:

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## Part 2 - lecture 2

Guaranteed numerical integration for initial value problems for ODEs.

Slides Practical work:

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## Part 2 - lecture 3

Guaranteed numerical integration for initial value problems for DAEs.

Slides Practical work:

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# Tools