# 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 N/A Natural & Applied Sciences Master's Degree Face To Face Lecture, Discussion, Question and Answer, Problem Solving. 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. 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. 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

### Sources

Course Book 1. [1] Numerical Solution of Differential Equations , M.K.Jain , Wiley Eastern Limited,1979. 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

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 100 100

### Course Category

Core Courses X

### 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 Has the ability to obtain, to evaluate, to interpret and to apply information by doing scientific research.
3 Can apply gained knowledge and problem solving abilities in inter-disciplinary research.
4 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.
5 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.
6 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework.
7 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility.
8 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.
9 Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields.
10 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge.
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.

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 16 3 48
Presentation/Seminar Prepration
Project
Report
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