 # Introduction to PDE based numerical models

## Presentation

Program (detailed contents):

Examples of PDE models: convection-diffusion equation, Black-Scholes equation …

Finite Difference Method and Monte-Carlo method for linear parabolic PDE.

Organisation:

Lectures : 11 slots

Tutorials : 4 lots

Labworks: 4 slots

Document: book of tutorials and labworks

## Objectives

At the end of this module, the student should have understood the following notions:

ü  Fundamentals of the Finite Difference Method (order of a scheme, stability, discrete maximum principle, convergence).

ü  Formal definition of the Brownian motion and principles of the Monte-Carlo method for parabolic PDE.

ü  The use of PDE for modelling problems with continuous variables.

The student will be able to:

-       Model simple problems using PDEs

-       Analyse stability and consistency of a finite difference scheme.

-       Program with MATLAB a finite difference scheme or the Monte-Carlo method for solving a linear parabolic PDE

-       Analyse numerical results and identify / explain numerical errors.

## Needed prerequisite

Basis of probability theory, integral and differential calculus & numerical analysis.

## Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...

## Additional information

Partial differential equation, finite difference method, Monte-Carlo method