# Numerical Solution of Ordinary Differential Equations (MAE744)

### General

School School of Science Department of Mathematics Undergraduate MAE744 7 Numerical Solution of Ordinary Differential Equations Lectures (Weekly Teaching Hours: 3, Credits: 6) Special background, skills development. - Greek Yes (in English) 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. 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

1. Initial Value Problems
2. Explicit Euler and Implicit Euler.
3. Consistency, stability, and convergence of Runge-Kutta methods.
4. Consistency, stability, and convergence of multistep methods.
5. Applications to ODEs systems arising from Physics and Biology.

### Teaching and Learning Methods - Evaluation

Delivery

Face-to-face.

Use of Information and Communications Technology
• Use of a tablet device to deliver teaching. Lecture materials in pdf-format are made available to students, for later review, on Moodle e-learning platform.
• Provision of study materials in Moodle e-learning platform.
• Provision of model solutions for some exercises in podcast format.
• Communication with students through e-mails, Moodle platform and Microsoft Teams.
• Use of sophisticated software (Python or Octave) for the implementation of the numerical algorithms.
Teaching Methods
Lectures 39
Study and analysis of bibliography 75
Directed study of Computer-based exercises 6
Non-directed study of Computer-based exercises 30
Course total 150
Student Performance Evaluation
• Computer-based exercises (organised in teams of 2) with oral examination (Weighting 30%, addressing learning outcomes 4-6)
• Written examination (Weighting 70%, addressing learning outcomes 1-4)

### 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.