Numerical Solution of Partial Differential Equations

Numerical solution of partial differential equations

Credits

Prerequisites

None

Scientific-disciplinary sector

MAT/08

Examination method

Oral exam and assessment of the laboratory work.

Learning objectives

The course concerns the study of methods and algorithms for the numerical solution of problems described by partial differential models. The main differential operators – elliptic, parabolic and hyperbolic – will be examined, and through the numerical and algorithmic analysis of the solution phases, the course aims to introduce students to the issues underlying the solution of application models.

Syllabus

Preliminary concepts and definitions on partial differential operators. Numerical solution of elliptic, parabolic and hyperbolic initial and boundary value problems. Finite difference and finite element approximation schemes for partial differential equations. Study of consistency, convergence and stability. Considerations on the use of the methods in cases not covered by the theory. Numerical solution of selected equations arising from applications.

Expected learning
outcomes

At the end of the course, students must demonstrate that they

know and understand the general issues concerning the analysis of methods for the numerical solution of partial differential operators,
can apply the knowledge acquired by independently designing numerical algorithms for numerical simulation models,
can communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences,
can identify the most appropriate methods to analyse and solve a problem related to the course topics and interpret the results correctly.

Learning outcomes
to be assessed

Analysis of the issues addressed during the course on a case study. Independence in preparing the case study. Clarity of exposition.

Numerical Solution of Partial Differential Equations