Nevşehir Hacı Bektaş Veli University Course Catalogue

Information Of Programmes

INSTITUTE OF SCIENCE / MAT662 - MATHEMATICS (DOCTORATE DEGREE)

Code: MAT662 Course Title: FINITE DIFFERENCE METHODS II Theoretical+Practice: 3+0 ECTS: 6
Year/Semester of Study 1 / Spring Semester
Level of Course 3rd Cycle Degree Programme
Type of Course Optional
Department MATHEMATICS (DOCTORATE DEGREE)
Pre-requisities and Co-requisites None
Mode of Delivery Face to Face
Teaching Period 14 Weeks
Name of Lecturer SEYDİ BATTAL GAZİ KARAKOÇ (sbgkarakoc@nevsehir.edu.tr)
Name of Lecturer(s) SEYDİ BATTAL GAZİ KARAKOÇ,
Language of Instruction Turkish
Work Placement(s) None
Objectives of the Course

Learning Outcomes PO MME
The students who succeeded in this course:
LO-1 Find the approximate solutions of the Parabolic equations with finite difference approach. Compute the solutions of the systems of linear differential equations with iterative methods. Apply the finite difference approach to two and three dimensional partial differential equations. PO-1 Students can design an original issue and explore new, different and / or comprehend complex issues.
PO-2 Students will understand all aspects of mathematics and deepen the knowledge level that can innovate in this field.
PO-4 At least one foreign language at an advanced level counterparts in written, oral and visual communicate and participate in academic discussions.
 		Examination
Performance Project
PO: Programme Outcomes
MME:Method of measurement & Evaluation

Course Contents
Weekly Course Content
Week Subject Learning Activities and Teaching Methods
1 Local Truncation Error Consistency Stability Convergence Lax's Equivalence Theorem Oral expression,question and answer, solving problem
2 Matrix Method Stability Analysis of Explicit Finite Difference Approach with Matrix Method Dirichlet Boundary Conditional Heat Conduction Problem Oral expression,question and answer, solving problem
3 Neumann Boundary Conditional Heat Conduction Problem Robin Boundary Conditional Heat Conduction Problem Oral expression,question and answer, solving problem
4 Stability Analysis of the Implicit Finite Difference Approach with Matrix Method Dirichlet Boundary Conditional Heat Conduction Problem Oral expression,question and answer, solving problem
5 Neumann Boundary Conditional Heat Conduction Problem Robin Boundary Conditional Heat Conduction Problem Oral expression,question and answer, solving problem
6 Stability Analysis of the Crank-Nicolson Finite Difference Approach with Matrix Method Dirichlet Boundary Conditional Heat Conduction Problem Oral expression,question and answer, solving problem
7 Neumann Boundary Conditional Heat Conduction Problem Robin Boundary Conditional Heat Conduction Problem Oral expression,question and answer, solving problem
8 mid-term exam
9 von Neumann (Fourier Series) Method Stability Analysis Using the von Neumann Method Oral expression,question and answer, solving problem
10 Stability Analysis of the Explicit Finite Difference Approach with the von Neumann Method Stability Analysis of the Implicit Finite Difference Approach with the von Neumann Method Oral expression,question and answer, solving problem
11 Crank-Nicolson Finite Difference Approach with von Neumann Method Stability Analysis Oral expression,question and answer, solving problem
12 Local Shear Error of Classical Finite Difference Methods Local Cutting Error of Explicit Finite Difference Approach Oral expression,question and answer, solving problem
13 Local Cutting Error of the Implicit Finite Difference Approach Local Cutting Error of Crank-Nicolson Finite Difference Approach Oral expression,question and answer, solving problem
14 Analysis of Explicit Implicit and Crank-Nicolson finite difference approximations for heat conduction problem by matrix and von Neumann methods determinations and numerical solutions Oral expression,question and answer, solving problem
15 Analysis of Explicit Implicit and Crank-Nicolson finite difference approximations for heat conduction problem by matrix and von Neumann methods determinations and numerical solutions Oral expression,question and answer, solving problem
16 final exam
Recommend Course Book / Supplementary Book/Reading
1 1. G. D. Smith “Numericel solution of partial differential equations” (Clarendon press-Oxford 1985).
2 2. D. M. Causon, C. G. Mingham “Introductory Finite Difference Methods for PDEs” (Ventus Publishing ApS, 2010)
3 3. P. G. Ciarlet, Jacques Louis Lions , Philippe G. Ciarlet , "Handbook of Numerical Analysis: Finite Difference Methods” (North-Holland March 1990).
Required Course instruments and materials
The books of lecture.

Assessment Methods
Type of Assessment Week Hours Weight(%)
mid-term exam 8 2 40
Other assessment methods
1.Oral Examination
2.Quiz
3.Laboratory exam
4.Presentation
5.Report
6.Workshop
7.Performance Project
8.Term Paper
9.Project
final exam 16 2 60

Student Work Load
Type of Work Weekly Hours Number of Weeks Work Load
Weekly Course Hours (Theoretical+Practice) 3 14 42
Outside Class
       a) Reading 3 14 42
       b) Search in internet/Library 2 7 14
       c) Performance Project 2 8 16
       d) Prepare a workshop/Presentation/Report 0
       e) Term paper/Project 0
Oral Examination 0
Quiz 0
Laboratory exam 0
Own study for mid-term exam 3 8 24
mid-term exam 2 1 2
Own study for final exam 3 15 45
final exam 2 1 2
0
0
Total work load; 187