- Docente: Germana Landi
- Credits: 6
- SSD: MAT/08
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
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from Feb 18, 2025 to May 30, 2025
Learning outcomes
At the end of the course, students thoroughly know the theoretical and computational properties of the principal numerical methods for initial value ordinary differential equations, and of some advanced numerical methods for partial differential equations. In particular, students are able to analyze the theoretical properties of numerical methods and to critically examine the computational results.
Course contents
Brief mentions of machine numbers and the numerical solution of linear systems of equations.
Newton method for nonlinear equations. Inexact Newton methods; quasi-Newton methods.
One-step and multistep methods for initial value problems. Convergence, consistency and zero-stability. Absolute stability. Stiff problems.
The course includes a laboratory activity in which the student will be able to put into practice and experiment the proposed computational methods.
Readings/Bibliography
R.J. LeVque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, 2007
D.F. Griffths and D.J. Higham. Numerical Methods for Ordinary Differential Equations: Initial Value Problems. Springer, 2010.
J. Nocedal, S. J. Wright. Numerical Optimization. Springer, 2006.
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
The exam consists of an oral test on the topics covered in class and on the exercises carried out in the calculation laboratory.
The oral test is structured to verify the knowledge and level of understanding of the topics covered during the course.
Particular attention is given to both the ability to communicate the subject critically and the use of appropriate mathematical language.
Teaching tools
Slides provided by the teacher. The teaching material will be available on the University of Bologna e-learning platform (https://virtuale.unibo.it).
Office hours
See the website of Germana Landi