# Numerical Solution of Differential Equations (MDES620) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Numerical Solution of Differential Equations MDES620 Elective Courses 3 0 0 3 5
Pre-requisite Course(s)
Math 276 Differential Equations
Course Language English Elective Courses Natural & Applied Sciences Master's Degree Face To Face Lecture, Discussion, Question and Answer, Problem Solving. This course is designed to give engineering students in graduate level the expertise necessary to understand and use computational methods for the approximate/numerical solution of differential equations problems that arise in many different fields of science. The students who succeeded in this course; At the end of the course the students are expected to: 1-Choose an efficient method to solve the differential equation(s) coming from a certain application field, 2- Investigate the stability and convergence properties of the methods, 3- Recognize some of the numerical difficulties that can occur when solving problems arising in scientific applications. Numerical solution of initial value problems; Euler, multistep and Runge-Kutta methods; numerical solution of boundary value problems; shooting and finite difference methods; stability, convergence and accuracy; numerical solution of partial differential equations; finite difference methods for parabolic, hyperbolic and elliptic equations; explic

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 1. Week Review to differential equations 2. Week Numerical solutions of initial value problems; Euler, multistep and Runge-Kutta methods 3. Week Numerical solutions of initial value problems; Euler, multistep and Runge-Kutta methods 4. Week Numerical solutions of boundary value problems; finite difference methods 5. Week Numerical solutions of boundary value problems; finite difference methods 6. Week Stability, convergence and accuracy of the numerical techniques given 7. Week Stability, convergence and accuracy of the numerical techniques given 8. Week Midterm Exam 9. Week Partial differential equations and their solutions 10. Week Numerical solution of partial differential equations; finite difference methods 11. Week Numerical solution of partial differential equations; finite difference methods 12. Week Numerical solution of parabolic, hyperbolic and elliptic equations by finite difference methods 13. Week Explicit and implicit methods, Crank-Nicolson method 14. Week Explicit and implicit methods, Crank-Nicolson method. System of ordinary differential equations 15. Week Convergence, stability and consistency analysis of the methods 16. Week Final Exam

### Sources

Course Book 1. 1. Numerical Solution of Partial Differential Equations by K.W. Morton and D.F. Mayers, Cambridge University Press, 1994. 2.Numerical Analysis of Differential Equations by A. Iserles, Cambridge University Press, 1996. 2. 1.Computer Methods for ODEs and Differential-Algebraic Equations by U.M. Ascher & L.R. Petzold, SIAM, 1998. 2.Numerical Solution of Partial Differential Equations: Finite Difference Methods by G.D. Smith, Clarendon Press, Oxford, 1985.

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 5 30
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 1 30
Final Exam/Final Jury 1 40
Toplam 7 100
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 An ability to apply advanced knowledge in computational and/or manufacturing technologies to solve manufacturing engineering problems .
2 An ability to define and analyze issues related with manufacturing technologies.
3 An ability to develop a solution based approach and a model for an engineering problem and design and manage an experiment.
4 An ability to design a comprehensive manufacturing system based on creative utilization of fundamental engineering principles while fulfilling sustainability in environment and manufacturability and economic constraints.
5 An ability to chose and use modern technologies and engineering tools for manufacturing engineering applications.
6 Ability to perform scientific research and/or carry out innovative projects that are within the scope of manufacturing engineering.
7 An ability to utilize information technologies efficiently to acquire datum and analyze critically, articulate the outcome and make decision accordingly.
8 An ability to attain self-confidence and necessary organizational work skills to participate in multi-diciplinary and interdiciplinary teams as well as act individually.
9 An ability to attain efficient communication skills in Turkish and English both verbally and orally.
10 An ability to reach knowledge and to attain life-long learning and self-improvement skills, to follow recent advances in science and technology.
11 An awareness and responsibility about professional, legal, ethical and social issues in manufacturing engineering.
12 An awareness about solution focused project and risk management, enterpreneurship, innovative and sustainable development.
13 An understanding on the effects of engineering applications on health, social and legal aspects at universal and local level during decision making process.

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 3 48
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 16 2 32
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 5 25
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 8 16
Prepration of Final Exams/Final Jury 1 10 10