Numerical Solution of Ordinary Differential Equations (MAE744): Διαφορά μεταξύ των αναθεωρήσεων

Αναθεώρηση της 00:02, 29 Σεπτεμβρίου 2022

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAE744
Semester	7
Course Title	Numerical Solution of Ordinary 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: describe the basic characteristics of single-step and multi-step methods and recognize their differences. apply a variety of techniques for the construction of single-step and multi-step methods. apply numerical analysis techniques to show consistency, stability, and convergence of numerical methods. be aware of the optimal order of accuracy of key numerical methods as well as the limitations that may be required in the discretization parameters to ensure stability. write code (in Python or Octave) for the implementation of explicit and implicit numerical methods and calculate their experimental order of convergence. write code in Python or Octave for the numerical approximation of the solution of ODEs models that describe a variety of real-world situations.
General Competences	Search for, analysis and synthesis of data and information, with the use of the necessary technology. Adapting to new situations. Decision-making. Teamwork. Production of free, creative, and inductive thinking. Promotion of analytical and synthetic thinking.

Syllabus

Difference Equations, Initial Value Problems, One step methods (Euler - explicit and implicit, Runge Kutta methods), Multiple steps methods (Adams-Bashforth, Adams-Moulton, Predictor-Corrector methods). Convergence, Stability, Compatibility, Stiff ODE systems, Boundary Value Problems, Shooting method, Finite differences, Eigenvalue problems.

Teaching and Learning Methods - Evaluation

Delivery

In class

Use of Information and Communications Technology

Use of computer (Mechanics) lab

Teaching Methods

Activity	Semester Workload
Lectures	39
Study of theory	78
Home exercises	33
Course total	150

Student Performance Evaluation

Weekly assignments
Final project
Written examination at the end of the semester

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:

“Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations”, E. Hairer, & C. Lubich, Springer, 2010.
“Numerical Methods for Ordinary Differential Equations: Initial Value Problems”, D.F. Griffiths, & D. J. Higham, Springer, 2010.

@@ Γραμμή 56: / Γραμμή 56: @@
 ! Learning outcomes
 |
-The course is an introduction to the basic methods for the numerical solution of ordinary differential equations. The objectives of the course are:
+Upon successful completion of the course, students will be able to:
-* Development of theoretical background in matters concerning the numerical solution of ordinary differential equations (ODEs) and ODE systems.
+# describe the basic characteristics of single-step and multi-step methods and recognize their differences.
-* Ability of using numerical methods for solving ODEs with computational programs that will help with the implementation, e.g. Mathematica, Matlab etc.
+# apply a variety of techniques for the construction of single-step and multi-step methods.
-* Upon completion of this course the student will be able to use numerical methods for solving mathematical problems that may not have analytical solution and further deepen the understanding of such methods.
+# apply numerical analysis techniques to show consistency, stability, and convergence of numerical methods.
+# be aware of the optimal order of accuracy of key numerical methods as well as the limitations that may be required in the discretization parameters to ensure stability.
+# write code (in Python or Octave) for the implementation of explicit and implicit numerical methods and calculate their experimental order of convergence.
+# write code in Python or Octave for the numerical approximation of the solution of ODEs models that describe a variety of real-world situations.
 |-
 ! General Competences
 |
-The course aims to enable undergraduate students to develop the ability to analyze and synthesize basic knowledge of Numerical Analysis with the help of computers to numerically solve difficult problems in mathematics and/or physics. This will give to the student the opportunity to work in an international environment.
+* Search for, analysis and synthesis of data and information, with the use of the necessary technology.
+* Adapting to new situations.
+* Decision-making.
+* Teamwork.
+* Production of free, creative, and inductive thinking.
+* Promotion of analytical and synthetic thinking.
 |}
 === Syllabus ===
 Difference Equations, Initial Value Problems, One step methods (Euler - explicit and implicit, Runge Kutta methods), Multiple steps methods (Adams-Bashforth, Adams-Moulton, Predictor-Corrector methods). Convergence, Stability, Compatibility, Stiff ODE systems, Boundary Value Problems, Shooting method, Finite differences, Eigenvalue problems.