Numerical Analysis 2
A.Y. 2025/2026
Learning objectives
Presentation of the most common methods for the numerical solution of ordinary differential equations and introduction in their error analysis.
Expected learning outcomes
The ability to assess, implement, and interpret the results of numerical methods for initial value problems.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
Introduction. Initial value problems, well-posedness, conditioning and regularity. One-step methods: consistency, stability, convergence, stiffness and integrals of motion.
There will be also an extension of 3 cfu with supplementary material, covering in particular multi-step methods.
There will be also an extension of 3 cfu with supplementary material, covering in particular multi-step methods.
Prerequisites for admission
Analysis and Linear Algebra. Basic knowledge of the programming language C.
Teaching methods
Lectures, exercises and lab sessions.
Teaching Resources
P. Deuflhard, F. Bornemann, Scientific computing with ordinary differential equations, Springer 2002
E. Hairer, S. P. Norsett, G. Wanner, Solving ordinary differential equations I. Nonstiff problems, 2nd edition, Springer 1993
E. Hairer, G. Wanner, Solving ordinary differential equations II. Stiff and differential-algebraic problems, 2nd edition, Springer, 1996
E. Hairer, S. P. Norsett, G. Wanner, Solving ordinary differential equations I. Nonstiff problems, 2nd edition, Springer 1993
E. Hairer, G. Wanner, Solving ordinary differential equations II. Stiff and differential-algebraic problems, 2nd edition, Springer, 1996
Assessment methods and Criteria
The examination consists of written part, which can be done in two different manners, and an oral exam on personal appointment.
The two options for the written part are:
1) Solve at least three problems among those that are foreseen for this purpose during the semester. The solutions have to be submitted within the comunicated dates. The submission has to be in electronic form or, only for theoretical problems, by hand. The solutions will be returned, outlining possible errors.
2) Solve a small project from a list that will be published at the beginning of each exam session. The project can be done with at most one other person. It has to be submitted by email at least one week before the oral exam and contains a summary on the project within 5 pdf pages.
For both options, the source codes (but no executables) of a required implementation have to be enclosed. Also, books and any other tools (including artificial intelligence) are allowed, under the condition that their use is declared or indicated by references.
The oral exam starts with the written part and may explore any its details. Subsequently, questions about any argument of the course may be asked. An oral exam cannot be repeated with the same written part. Final marks will be communicated after the oral examination and are given using the numerical range 0-30, where passing corresponds to >17.
In order to arrange the date of the oral exam, the student has to enroll in the timewise-closest "appello". Please observe that not all dates will be available. During June and July, the dates of the "appelli" are guaranteed.
The two options for the written part are:
1) Solve at least three problems among those that are foreseen for this purpose during the semester. The solutions have to be submitted within the comunicated dates. The submission has to be in electronic form or, only for theoretical problems, by hand. The solutions will be returned, outlining possible errors.
2) Solve a small project from a list that will be published at the beginning of each exam session. The project can be done with at most one other person. It has to be submitted by email at least one week before the oral exam and contains a summary on the project within 5 pdf pages.
For both options, the source codes (but no executables) of a required implementation have to be enclosed. Also, books and any other tools (including artificial intelligence) are allowed, under the condition that their use is declared or indicated by references.
The oral exam starts with the written part and may explore any its details. Subsequently, questions about any argument of the course may be asked. An oral exam cannot be repeated with the same written part. Final marks will be communicated after the oral examination and are given using the numerical range 0-30, where passing corresponds to >17.
In order to arrange the date of the oral exam, the student has to enroll in the timewise-closest "appello". Please observe that not all dates will be available. During June and July, the dates of the "appelli" are guaranteed.
MAT/08 - NUMERICAL ANALYSIS - University credits: 6
Practicals: 24 hours
Laboratories: 12 hours
Lessons: 27 hours
Laboratories: 12 hours
Lessons: 27 hours
Professors:
Veeser Andreas, Zanotti Pietro
Educational website(s)
Professor(s)