ECTS - Numerical Methods for Ordinary Differential Equations

Numerical Methods for Ordinary Differential Equations (MATH482) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Numerical Methods for Ordinary Differential Equations MATH482 3 0 0 3 6
Pre-requisite Course(s)
MATH 382 Numerical Analysis
Course Language English
Course Type N/A
Course Level Bachelor’s Degree (First Cycle)
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture, Discussion, Question and Answer, Problem Solving.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives This course is designed to give the students the basic theory of numerical methods for solving Ordinary Differential Equations. In the course , first, the derivation, stability and convergence analysis of the methods for Initial Value Problems will be discussed , and than short introduction to the numerical methods for solving Boundary Value Problems will be given.
Course Learning Outcomes The students who succeeded in this course;
  • At the end of the course the students are expected to: 1) derive some practical numerical methods for solving initial and boundary value problems in ordinary differential equations, 2) investigate the stability and convergence properties of the methods, 3) identify numerical methods that best approximates the solution of the problem, 4) recognise some of the numerical difficulties that can occur when solving differential equations arising in applications.
Course Content Existence, uniqueness and stability theory; IVP: Euler?s method, Taylor series method, Runge-Kutta methods, explicit and implicit methods; multistep methods based on integration and differentiation; predictor?corrector methods; stability, convergence and error estimates of the methods; boundary value problems: finite difference methods, shooting me

Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 1. Week Existence, Uniqueness and Stability Theory. 2. Week One-Step Methods: Euler’s Method , Taylor Series Method. 3. Week One-Step Methods: General Theory of Runge - Kutta Methods 4. Week One-Step Methods: Derivation and Error Analysis of Explicit Runge - Kutta Methods. 5. Week One-Step Methods: Derivation and Error Analysis of Implicit Runge - Kutta Methods. 6. Week One-Step Methods: Stability and Convergence Analysis 7. Week Multistep Methods:. Derivations of Explicit Multistep Methods , Error and Convergence Analysis. 8. Week Midterm Exam 9. Week Multistep Methods: Derivations of Implicit Multistep Methods , Error and Convergence Analysis. 10. Week Multistep Methods: Multistep Methods Based on Differentiation. 11. Week Multistep Methods: Relative and Absolute Stability of Multistep Methods. 12. Week Multistep Methods: Predictor – Corrector Methods. 13. Week Boundary Value Problems : Finite Difference Methods. 14. Week Boundary Value Problems : Shooting Methods. 15. Week Boundary Value Problems : Collocation Methods. 16. Week Final Exam


Course Book 1. [1] Numerical Solution of Differential Equations , M.K.Jain , Wiley Eastern Limited,1979.
Other Sources 2. [2] Numerical Analysis, by D. Kincaid & Ward Cheney Brooks/Cole Publishing Company , 1991. [3] Numerical Analysis, by L.W.Johnson & R.D.Riess, Addison Wesley, 1982. [4] An Introduction to Numerical Analysis, by K.E.Atkinson, John Wiley and Sons,1999

Evaluation System

Requirements Number Percentage of Grade
Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 3 20
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 40
Final Exam/Final Jury 1 40
Toplam 6 100
Percentage of Semester Work
Percentage of Final Work 100
Total 100

Course Category

Core Courses
Major Area Courses X
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research
3 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary
4 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility
7 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2)
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach.
11 Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications.

ECTS/Workload Table

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Special Course Internship
Field Work
Study Hours Out of Class 16 3 48
Presentation/Seminar Prepration
Homework Assignments 3 10 30
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 16 32
Prepration of Final Exams/Final Jury 1 24 24
Total Workload 134