ECTSNumerical Solution of Differential Equations

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
Course Type Elective Courses
Course Level Natural & Applied Sciences Master's Degree
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 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.
Course Learning Outcomes 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.
Course Content 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.
Other Sources 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

Requirements Number Percentage of Grade
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
Percentage of Final Work 100
Total 100

Course Category

Core Courses X
Major Area Courses
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 An ability to access, analyze and evaluate the knowledge needed for the solution of advanced chemical engineering and applied chemistry problems.
2 An ability to self-renewal by following scientific and technological developments within the philosophy of lifelong learning.
3 An understanding of social, environmental, and the global impacts of the practices and innovations brought by chemistry and chemical engineering.
4 An ability to perform original research and development activities and to convert the achieved results to publications, patents and technology.
5 An ability to apply advanced mathematics, science and engineering knowledge to advanced engineering problems.
6 An ability to design and conduct scientific and technological experiments in lab- and pilot-scale, and to analyze and interpret their results.
7 Skills in design of a system, part of a system or a process with desired properties and to implement industry.
8 Ability to perform independent research.
9 Ability to work in a multi-disciplinary environment and to work as a part of a team.
10 An understanding of the professional and occupational responsibilities.

ECTS/Workload Table

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
Total Workload 131