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.

Readings/Bibliography

• 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 and computer Laboratory

Assessment methods

Project and oral discussion

Teaching tools

e-learning platform: Virtuale

Office hours

See the website of Fabiana Zama