Nevşehir Hacı Bektaş Veli University Course Catalogue

Information Of Programmes

FACULTY OF LETTERS & SCIENCE / MAT483 - MATHEMATICS

Code: MAT483 Course Title: INTRODUCTION TO FINITE DIFFERENCE METHODS Theoretical+Practice: 4+0 ECTS: 6
Year/Semester of Study 4 / Fall Semester
Level of Course 1st Cycle Degree Programme
Type of Course Optional
Department MATHEMATICS
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)
Language of Instruction Turkish
Work Placement(s) None
Objectives of the Course
The aim of this course is to obtain approximate solutions of partial differential equations with finite difference methods.

Learning Outcomes PO MME
The students who succeeded in this course:
PO: Programme Outcomes
MME:Method of measurement & Evaluation

Course Contents
Classification of partial differential equations, finite difference approaches for partial derivatives, solution of elliptic partial differential equations with finite difference methods, concepts of consistency, stability and convergence, Lax's equality theory, spectral radius, solution of parabolic partial differential equations with finite difference methods, explicit, implicit and Crank-Nicolson methods for heat equation, stability analysis of methods, solution of hyperbolic partial differential equations with finite difference methods.
Weekly Course Content
Week Subject Learning Activities and Teaching Methods
1 Classification of partial differential equations (Parabolic, Hyperbolic and Elliptic Types). Narrative and Problem Solving Methods.
2 Matrix and vector norms Narrative and Problem Solving Methods.
3 1st and 2nd Gershgorin Theorems Narrative and Problem Solving Methods.
4 Gershgorin's Circle Theory. Narrative and Problem Solving Methods.
5 Difference Equations Narrative and Problem Solving Methods.
6 Finite difference approaches for the first order derivatives. Narrative and Problem Solving Methods.
7 Finite difference approaches for the second order derivatives. Narrative and Problem Solving Methods.
8 mid-term exam
9 Finite difference indication of time dependent heat transfer equation. Narrative and Problem Solving Methods.
10 Solution of time dependent heat transfer equation with explicit difference method. Narrative and Problem Solving Methods.
11 Consistency, stability and convergence. Lax's equality theory. Narrative and Problem Solving Methods.
12 Spectral radius. Local truncation error. Narrative and Problem Solving Methods.
13 solution of parabolic partial differential equations with finite difference methods Narrative and Problem Solving Methods.
14 Explicit and implicit methods for heat equation. Narrative and Problem Solving Methods.
15 Crank-Nicolson method for heat equation. Narrative and Problem Solving Methods.
16 final exam
Recommend Course Book / Supplementary Book/Reading
1 Numerical Solution of Partial Differential Equations Leon LAPIDUS and George F. PINDER. Numerical Solution of Partial Differential Equations: Finite Difference Methods G. D. Smith, Gordon D. Smith Numerical Solution of Partial Differential Equations K. W
Required Course instruments and materials

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) 4 14 56
Outside Class
       a) Reading 4 14 56
       b) Search in internet/Library 2 14 28
       c) Performance Project 0
       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 4 4 16
mid-term exam 2 1 2
Own study for final exam 5 4 20
final exam 2 1 2
0
0
Total work load; 180