Finite Difference Methods
Mathematics
Institute of Natural and Applied Sciences
Second Cycle (Master's Degree)
| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Finite Difference Methods | MAT527 | Elective | Master's degree | 1 | Spring | 8 |
Name of Lecturer(s)
Prof. Dr. Vildan GÜLKAÇ
Learning Outcomes of the Course Unit
1) Defining how can use finite difference equation for partial differential equation in the solution mathematics, physics and engineerings.
2) explain the notion of finite difference and define how to apply.
3) explain the notion of expilicit finite difference equation and defines how to analyze the convergence of them.
4) Explain the notion of implicit finite difference equation and define how to analyze the convergence of them.
5) Explain the notion of Crank-Nicolson difference equation and define how to analyze the convergence of them.
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
| Learning Outcomes | ||||||||
| 1 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 3 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 4 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 5 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Not Required
Course Contents
Finite-diffrence approximations to derivatives, parabolic equations, hyperbolic equations, elliptic equations
Weekly Schedule
1) Finite-difference approximations to derivatives2) parabolic equations, explicit method
3) Crank- Nicolson implicit method
4) Iterative point methods for solving the finite difference equations of implicit methods
5) Derivative boundary conditions
6) The parabolic equation in cylindirical and spherical polar coordinates
7) exercises and solutions
8) Midterm examination/Assessment
9) Convergence, stability, and systematic iterative methods
10) Compatibility
11) General treatment of systematic iterative methods for linear equations
12) exercises and solutions
13) Hyperbolic equations
14) Elliptic equations
15) -----
16) Final examination
Recommended or Required Reading
1- Numerical Solution of partial differential equations Finite Difference Methods
G.D Smith, Clarendon Press- Oxford
2- Professor D. M. Causon; Professor C. G. Mingham
Introductory Finite Difference Methods for PDEs
3- Randall LeVeque ,Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems (Classics in Applied Mathematic) [Paperback]
4-
John C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, 2nd Edition
5- Numerical Solution of partial differential equations Finite Difference Methods
G.D Smith, Clarendon Press- Oxford
6- Numerical Solution of partial differential equations Finite Difference Methods
G.D Smith, Clarendon Press- Oxford
7- problemler
8- exercises
9- sözlü
10- quiz
Planned Learning Activities and Teaching Methods
1) Lecture
2) Discussion
3) Demonstration
4) Group Study
5) Problem Solving
Assessment Methods and Criteria
Contribution of Midterm Examination to Course Grade |
50% |
|---|---|
Contribution of Final Examination to Course Grade |
50% |
Total |
100% |
Language of Instruction
Turkish
Work Placement(s)
Not Required