Numerical Solution of Ordinary Differential Equations (MAE744)

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

The course is an introduction to the basic methods for the numerical solution of ordinary differential equations. The objectives of the course are: Development of theoretical background in matters concerning the numerical solution of ordinary differential equations (ODEs) and ODE systems. Ability of using numerical methods for solving ODEs with computational programs that will help with the implementation, e.g. Mathematica, Matlab etc. 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.

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.

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.