Finite Difference Methods for Partial Differential Equations
Course Code
Semester
Course Name
LE/RC/LA
Course Type
Language of Instruction
ECTS
YMB0009
Finite Difference Methods for Partial Differential Equations
3/0/0
DE
Turkish
7
Course Goals
To understand basic finite difference methods for partial differential equations
Prerequisite(s)
Matlab
Corequisite(s)
None.
Special Requisite(s)
The minimum qualifications that are expected from the students who want to attend the course.(Examples: Foreign language level, attendance, known theoretical pre-qualifications, etc.)
Instructor(s)
Assist. Prof. Dr. Hikmet ÇAĞLAR
Course Assistant(s)
None.
Schedule
Will be announced in the forthcoming term.
Office Hour(s)
Yrd. Doç. Dr. Hikmet ÇAĞLAR, AK/3-A-09.
Teaching Methods and Techniques
Lecture and homeworks.
Principle Sources
Finite Difference Methods for Ordinary and Partial Differential Equations, R. J. LeVeque, SIAM 2007
Other Sources
-
Course Schedules
Week
Contents
Learning Methods
1. Week
Classification of partial differential equations into hyperbolic, parabolic, and elliptic types
Lecture
2. Week
Review of finite-difference
approximations
Lecture
3. Week
Finite difference methods
Lecture
4. Week
Finite difference methods
Lecture
5. Week
Consistency, stability, and convergence
Lecture
6. Week
Consistency, stability, and convergence
Lecture
7. Week
Consistency, stability, and convergence
Lecture
8. Week
Midterm Exam
Midterm Exam
9. Week
Hyperbolic Partial Differential Equations
Lecture
10. Week
Hyperbolic Partial Differential Equations
Lecture
11. Week
Parabolic Partial Differential Equations
Lecture
12. Week
Parabolic Partial Differential Equations
Lecture
13. Week
Elliptic Partial Differential Equations
Lecture
14. Week
Elliptic Partial Differential Equations
Lecture
15. Week
Final Exam Week
Final Exam
16. Week
Final Exam Week
Final Exam
17. Week
Final Exam Week
Final Exam
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
50
Final Exam
1
50
Program Outcomes
PO-1
Have scientific research in mathematics and computer science in the level of theoretical and practical knowledge.
PO-2
On the basis of undergraduate level qualifications, develop and deepen the same or a different areas of information at the level of expertise, and analyze and interpret by using statistical methods
PO-3
Develop new strategic approaches for the solution of complex problems encountered in applications related to the field and unforeseen and take responsibility for the solution.
PO-4
Evaluate critically skills acquired in the field of information in the level of expertise and assess the learning guides.
PO-5
Transfer current developments in the field and their work to the groups inside and outside the area supporting with quantitative and qualitative datas as written, verbal and visual by a systematic way.
PO-6
Use information and communication technologies with computer software in advanced level.
PO-7
Develop efficient algorithms by modeling problems faced in the field and solve such problems by using actual programming languages.
PO-8
Respect to social, scientific, cultural and ethical values at the stages of data collection related to the field, interpretation, and implementation.
PO-9
To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-10
Establish and discuss in written, oral and visual communication in an advanced level by using at least one foreign language.
Learning Outcomes
LO-1
Classify diferantiel equation
LO-2
Construct appropriate finite-difference approximations to PDEs
LO-3
Show that a finite difference method is consistent
LO-4
Find the order of accuracy of a finite difference method
LO-5
Write Matlab programs to solve linear differantiel equation by finite difference methods
LO-6
Verify experimentally the convergence and accuracy of numerical methods
