Numerical Solution of Partial Differential Equations (MAE882): Διαφορά μεταξύ των αναθεωρήσεων
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* [[Αριθμητική Επίλυση Διαφορικών Εξισώσεων με Μερικές Παραγώγους ( | * [[Αριθμητική Επίλυση Διαφορικών Εξισώσεων με Μερικές Παραγώγους (ΜΑΕ882)|Ελληνική Έκδοση]] | ||
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MAE882 | |||
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Τελευταία αναθεώρηση της 13:29, 12 Δεκεμβρίου 2023
- Ελληνική Έκδοση
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General
School |
School of Science |
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Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE882 |
Semester |
8 |
Course Title |
Numerical Solution of Partial Differential Equations |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special background, skills development. |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Upon successful completion of the course, students will be able to:
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General Competences |
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Syllabus
- Finite difference approximations to derivatives.
- The two-point boundary value problem. Boundary conditions of type Dirichlet, Neumann, and Robin.
- Finite differences schemes for the two-point boundary value problem. Consistency and stability. The energy method. Order of accuracy and convergence.
- The Finite Element Method (FEM) for the two-point boundary value problem. A priori and a posteriori estimates. Implementation of FEM.
- Finite differences and Finite element methods for the Heat Equation in 1D. Explicit- and implicit Euler, the Crank-Nicolson method. Consistency and stability.
- The finite element method for elliptic and parabolic equations in higher dimensions.
Teaching and Learning Methods - Evaluation
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Teaching Methods |
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Student Performance Evaluation |
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Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- “Αριθμητική επίλυση μερικών διαφορικών εξισώσεων”, Π. Χατζηπαντελίδης, & Μ. Πλεξουσάκης, Κάλλιπος, (2015). http://hdl.handle.net/11419/665
- “Αριθμητικές Μέθοδοι για Συνήθεις Διαφορικές Εξισώσεις”, Γ. Δ. Ακρίβης, & Β. Α. Δουγαλής., Πανεπιστημιακές Εκδόσεις Κρήτης, Ηράκλειο, 2η έκδοση, 2013.
- “The mathematical theory of finite element methods”, S. C. Brenner & L. R. Scott (Third ed., Vol. 15), Springer, New York, 2008.
- “Partial differential equations with numerical methods”, S. Larsson, & V. Thomée, Springer-Verlag, Berlin, 2009.