Advanced Engineering Analysis

Dates: 8, 9 and 10 July 2024
Morning Session (Theory) 9:30 – 12:30
Afternoon Session (Practical Exercises) 14:30 – 17:30

Introduction to Finite Difference Analysis

The aim of this course is to provide the basis for the finite difference analysis. This powerful tool may be adopted for a large number of engineering problems. The course is structured so to give to aQendants a general overview of the methods which may be used while facing up with a differenRal equaRon (both ordinary and parRal). More specifically the first part of the course is addressed to the definiRon of the discrete forms of derivaRves which are most commonly used in applicaRons. AUer, the Ordinary DifferenRal EquaRons (ODE’s) have analysed with referring both to Boundary Values Problems as well as to IniRal Values Problems. ODE’s have solved in case of system of equaRons as well, and the way to pass from a high order equaRon to a system of first order ones is presented as well. Thus, the focus moves towards the numerical soluRon of ParRal DifferenRal EquaRons (PDE’s) both at steady state and during transients. ParRcular aQenRon has addressed to the disRncRon between explicit and implicit methods with defining to stability condiRons when needed.

The course is organized in 6 lessons (expected duraRon 3h/each). The first part is purely theoreRcal, while within the second one some applicaRons will be developed. It is warmly suggested to have at least one laptop every two students. The exercises will be developed in Matlab.

Students’ a+endance will be monitored during the course execu7on – 75% minimum a+endance is required for the access to the final exam.
At the end of the course an exam is mandatory to achieve the posi7ve fulfilment (discussion of self-developed exercises – PowerPoint presenta7on).
To join the course, please send an email to daniele.chiappini@unicusano.it

Total expected duraRon 18 h – 6CFU
Table of contents:
• IntroducRon to numerical methods;
• SoluRon of Ordinary DifferenRal EquaRons;
• SoluRon of System of Ordinary DifferenRal EquaRons
• SoluRon of EllipRc EquaRons
• IteraRve SoluRon of Linear Systems
• SoluRon of Parabolic EquaRons – 1D case
• SoluRon of Parabolic EquaRons – 2D case
• SoluRon of Hyperbolic EquaRons – 1D case
• SoluRon of Hyperbolic EquaRons – 2D case

info