96765 - Numerical Differential Equations

Learning outcomes

At the end of the course, students know advanced methods for the numerical treatment of partial differential problems in two and three dimensions. In particular, students are able to examine the construction, the convergence and the implementation details of the principal methods associated with the numerical solution of important model problems occurring in scientific and social applications.

Course contents

• General principles of the numerical solution of Partial Differential Equations by finite differences and finite elements schemes.
• Algorithmic details related to the numerical solution of stationary Diffusion-Transport, Diffusion Reaction equations.
• Algorithmic details of numerical methods for time dependent PDEs.

The course focuses on the algorithmic analysis of the proposed methods requiring to write MATLAB codes and examining existing libraries.

Prerequisites

- Matlab programming

- Floating point arithmetic.
- Numerical methods for the solution of linear systems;

- Numerical methods for the solution of nonlinear equations.
- Data approximation: polynomial and piecewise polynomial functions; interpolation and least-squares approximation.
- Numerical integration: Newton-Cotes quadrature formulas.

-Numerical Methods for ODE Initial value problems and boundary value problems.

Readings/Bibliography

• Larsson S. and Thomee V. Partial differential equations with numerical methods, volume 45. Springer, 2003.
• Thomas, J. W.: Numerical Partial Differential Equations. Finite Difference Methods. New York etc., Springer-Verlag 1995
• Thomas, J. W.: Numerical Partial Differential Equations. Conservation Laws and Elliptic Equations. New York etc., Springer-Verlag 1995
• Johnson, C. Numerical Solution of Partial Differential Equations by the Finite Element Method, Dover publications, 2009.

Teaching methods

Classroom lectures for the theory, and computer Laboratory for codes implementation and analysis of proposed examples.

In consideration of the type of activity and teaching methods adopted, the frequency of this training activity requires the prior participation of all students in Modules 1 and 2 of safety training in the places of study, in e-learning mode.

Assessment methods

- Project be presented orally at the end of the course or submitted successively as a written report.

- Oral about theory and laboratory examples.

Teaching tools

e-learning platform: Virtuale

Office hours

See the website of Fabiana Zama