| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT6018 | Numerical Solutions of Differential Equations II | Fall | 3 | 0 | 3 | 12 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | Tr |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Assoc. Prof. ERSİN ÖZUĞURLU |
| Course Objectives: | To see the applications and numerical solution of the partial differential equations. |
|
The students who have succeeded in this course; The students who succeeded in this course; o will be able to understand basic finite difference methods for partial differential equations. o will be able to solve numerically any given linear or nonlinear partial differential equation. o will be able to understand the concepts of consistency, stability, and convergence. o will be able to solve partial differential equations bu using using a computer program (C, C , Fortran, Matlab). o will be able to discuss the consistency, convergence and stability for schemes. o will be able to do error analysis. |
| This course focuses on the fundamentals of modern and classical numerical techniques for linear and nonlinear partial differential equations, with application to a wide variety of problems in science, engineering and other fields. The course covers the basic theory of scheme consistency, convergence and stability and various numerical methods. |
| Week | Subject | Related Preparation | |
| 1) | Hyperbolic Partial Differential Equations: Finite difference methods. | ||
| 2) | Consistency, stability, and convergence | ||
| 3) | The Lax Richtmyer equivalence theorem | ||
| 4) | The Courant Friedrichs Lewy condition. Von Neumann Analysis | ||
| 5) | Order of accuracy Multistep schemes. Dissipation and dispersion. | ||
| 6) | Parabolic Partial Differential Equations: Finite difference methods | ||
| 7) | Parabolic systems in higher dimensions | ||
| 8) | ADI methods | ||
| 9) | Elliptic Partial Differential Equations: Regularity and maximum principles | ||
| 10) | Finite difference methods, Linear iterative methods. | ||
| 11) | Multigrid methods | ||
| 12) | Rigorous convergence analysis | ||
| 13) | Error estimates | ||
| 14) | Matrix method for stability analysis, Spectral methods | ||
| Course Notes: | Partial Differential Equations with Boundary Value Problems by Larry C. Andrews. Numerical Solution of Partial Differentail Equations by K.W. Morton and D.F. Mayers Numerical Solution of Partial Differential Equations: Finite Difference Methods by G.D. Smith |
| References: | Partial Differential Equations. Lawrence C. Evans Applied Partial Differential Equations Paul DuChateau, David Zachmann Applied Partial Differential Equations Richard Haberman Applied Partial Differential Equations John R. Ockendon, Sam Howison, John Ockendon, Andrew Lacey, Alexander Movchan |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | 5 | % 15 |
| Homework Assignments | % 0 | |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 2 | % 45 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 40 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 60 | |
| PERCENTAGE OF FINAL WORK | % 40 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 14 | 5 | 70 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 5 | 5 | 25 |
| Preliminary Jury | 0 | ||
| Midterms | 2 | 20 | 40 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 23 | 23 |
| Total Workload | 200 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |