ECTS - Numerical 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 | Area Elective | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Core Course |
| Course Level | Ph.D. |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture. |
| Course Lecturer(s) |
|
| 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;
|
| 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 | Review to differential equations | Read related sections in references |
| 2 | Numerical solutions of initial value problems; Euler, multistep and Runge-Kutta methods | Read related sections in references |
| 3 | Numerical solutions of initial value problems; Euler, multistep and Runge-Kutta methods | Read related sections in references |
| 4 | Numerical solutions of boundary value problems; Shooting and finite difference methods | Read related sections in references |
| 5 | Numerical solutions of boundary value problems; Shooting and finite difference methods | Read related sections in references |
| 6 | Stability, convergence and accuracy of the numerical techniques given | Read related sections in references |
| 7 | Stability, convergence and accuracy of the numerical techniques given | Read related sections in references |
| 8 | Partial differential equations and their solutions | Read related sections in references |
| 9 | Numerical solution of partial differential equations; finite difference methods | Read related sections in references |
| 10 | Numerical solution of partial differential equations; finite difference methods | Read related sections in references |
| 11 | Numerical solution of parabolic, hyperbolic and elliptic equations by finite difference methods | Read related sections in references |
| 12 | Explicit and implicit methods, Crank-Nicolson method | Read related sections in references |
| 13 | Explicit and implicit methods, Crank-Nicolson method. System of ordinary differential equations | Read related sections in references |
| 14 | Convergence, stability and consistency analysis of the methods | Read related sections in references |
| 15 | Overall review | - |
| 16 | Final exam | - |
Sources
| Course Book | 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 | 3. Numerical Solution of Partial Differential Equations: Finite Difference Methods by G.D. Smith, Clarendon Press, Oxford, 1985. |
| 4. Computer Methods for ODEs and Differential-Algebraic Equations by U.M. Ascher & L.R. Petzold, SIAM, 1998. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 5 | 18 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 42 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 8 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| 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 | Ability to carry out advanced research activities, both individual and as a member of a team | X | ||||
| 2 | Ability to evaluate research topics and comment with scientific reasoning | X | ||||
| 3 | Ability to initiate and create new methodologies, implement them on novel research areas and topics | X | ||||
| 4 | Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions | X | ||||
| 5 | Ability to apply scientific philosophy on analysis, modelling and design of engineering systems | X | ||||
| 6 | Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level | X | ||||
| 7 | Contribute scientific and technological advancements on engineering domain of his/her interest area | X | ||||
| 8 | Contribute industrial and scientific advancements to improve the society through research activities | X | ||||
ECTS/Workload Table
| 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 | 5 | 80 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 5 | 10 | 50 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 15 | 30 |
| Prepration of Final Exams/Final Jury | |||
| Total Workload | 160 | ||