Advanced Numerical Analysis and Scientific Computing
| Title | ΠΡΟΧΩΡΗΜΕΝΗ ΑΡΙΘΜΗΤΙΚΗ ΑΝΑΛΥΣΗ ΚΑΙ ΕΠΙΣΤΗΜΟΝΙΚΟΣ ΥΠΟΛΟΓΙΣΜΟΣ / Advanced Numerical Analysis and Scientific Computing |
| Code | ΣΜΥ030 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Efthymios Karatzas |
| Common | Yes |
| Status | Active |
| Course ID | 600025966 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| STATISTIKĪ, MONTELOPOIĪSĪ KAI YPOLOGISTIKES METHODOI | Elective Courses belonging to the selected specialization | Winter | - | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Winter |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600268413
|
Course Type 2021
General Foundation
Course Type 2016-2020
- Background
Mode of Delivery
- Face to face
Digital Course Content
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Instruction, Examination)
Prerequisites
General Prerequisites
Fundamental numerical and mathematical analysis and a programming language knowledge.
Learning Outcomes
Upon successful completion of the course, students should understand initial value problems and be able to analyze and solve differential equations as well as systems of linear differential equations. Understand the role of continuous problem stability, order of accuracy and various stability properties of numerical methods for initial value problems. Know the basic numerical methods for initial value problems, as well as their advantages and disadvantages. To be able to implement the aforementioned methods on the computer.
General Competences
- Apply knowledge in practice
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Adapt to new situations
- Work autonomously
- Work in teams
- Work in an interdisciplinary team
Course Content (Syllabus)
Initial-value and boundary-value problems. Numerical methods for solving ordinary differential equations with initial conditions and/or boundary conditions. Linear and non-linear Shooting methods. Linear and non-linear finite difference methods. Calculus of variations techniques. Introduction to finite element method. Finite element methods for elliptic, parabolic, and hyperbolic problems.
Keywords
Numerical Analysis, Numerical Analysis for Partial Defferential Equations.
Educational Material Types
- Slide presentations
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Laboratory Teaching
- Use of ICT in Communication with Students
Description
Slides projector, computer.
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 75 | ||||
| Seminars | 25 | ||||
| Laboratory Work | 50 | ||||
| Reading Assigment | 150 | ||||
| Exams | 0 | ||||
| Total | 300 |
Student Assessment
Description
Αssignment, presentation of assignment, written exams.
Student Assessment methods
- Written Exam with Short Answer Questions (Formative)
- Written Exam with Extended Answer Questions (Formative)
- Written Assignment (Formative)
- Oral Exams (Summative)
- Performance / Staging (Summative)
- Written Exam with Problem Solving (Formative)
- Report (Summative)
Bibliography
Course Bibliography (Eudoxus)
-Αριθμητικές Μέθοδοι για Συνήθεις Διαφορικές Εξισώσεις, Γ. Δ. Ακρίβη και Β. Α. Δουγαλή, Πανεπιστημιακές Εκδόσεις Κρήτης, Ηράκλειο, δεύτερη έκδοση, 2013.
-Αριθμητική Ανάλυση: Συνήθεις Διαφορικές Εξισώσεις, Μ. Ν. Βραχάτη, Εκδόσεις Κλειδάριθμος, Αθήνα, 2012.
Additional bibliography for study
[1] R. Johansson, Numerical Python, Second Edition, Apress, 2019.
[2] M. G. Larson and F. Bengzon, The Finite Element Method: Theory, Implementation, and Applications, Springer, 2013.
[3] A. Friedman, C. Y. Kao, “Mathematical Modeling of Biological Processes”, Springer International Publishing, 2014.
[4] M. Asch, “A Toolbox for Digital Twins : From Model-Based to Data-Driven” Society for Industrial and Applied Mathematics SIAM, Philadelphia, 2022.
[5] H. P. Langtangen and A. Logg, Solving PDEs in Python, The FEniCS Tutorial I, Springer, 2016.
[6] E. N. Karatzas, G. Stabile, F. Ballarin, and G. Rozza, Book chapter In Advanced Reduced Order Methods and Applications in Computational Fluid Dynamics: “Reduced Basis, Embedded Methods, and Parametrized Level-Set Geometry”, SIAM Computational Science and Engineering, 2022.
Last Update
15-09-2025
