Nevşehir Hacı Bektaş Veli University Course Catalogue

Information Of Programmes

INSTITUTE OF SCIENCE / MAT582 - MATHEMATICS

Code: MAT582 Course Title: NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS Theoretical+Practice: 3+0 ECTS: 6
Year/Semester of Study 1 / Spring Semester
Level of Course 2nd 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 gain knowledge of numerical solution methods in partial differential equations (behavioral forms of parabolic, hyperbolic and elliptic differential equations).

Learning Outcomes PO MME
The students who succeeded in this course:
LO-1 PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems.
PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other.
PO-16 Ability to use the approaches and knowledge of other disciplines in Mathematics.
PO-17 Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.
 		Examination
PO: Programme Outcomes
MME:Method of measurement & Evaluation

Course Contents
Basic concepts, definition of partial differential equations, types of partial differential equations, finite difference method; discrete calculations, convergence to differentiation, differential representations of partial differential equations, convergence of finite difference method, stability and consistency and correctness of solution, parabolic equations; one dimensional diffusion equation, heat equation, general linear parabolic equations, nonlinear parabolic equations, hyperbolic equations; one dimensional wave equations, two dimensional wave equation, one dimensional quasilineer hyperbolic equations, Elliptic equations; Laplace equation, error analysis using maximum pyramid, finite volume method, finite element method, scattering methods. Multi-grid techniques, Finite element method, scattering methods.
Weekly Course Content
Week Subject Learning Activities and Teaching Methods
1 Basic concepts, definition of partial differential equations, types of partial differential equations. Oral expression, Problem solving method.
2 Finite difference method; discrete calculations, convergence to derivatives, differential representations of partial differential equations. Oral expression, Problem solving method.
3 Finite difference method; discrete calculations, convergence to derivatives, differential representations of partial differential equations. Oral expression, Problem solving method.
4 Convergence, Stability and Consistency of the Finite Difference Method and the Correctness of the Solution. Oral expression, Problem solving method.
5 Convergence, Stability and Consistency of the Finite Difference Method and the Correctness of the Solution. Oral expression, Problem solving method.
6 Parabolic equations; one dimensional diffusion equation, heat equation, general linear parabolic equations, nonlinear parabolic equations. Oral expression, Problem solving method.
7 Parabolic equations; one dimensional diffusion equation, heat equation, general linear parabolic equations, nonlinear parabolic equations. Oral expression, Problem solving method.
8 mid-term exam
9 Hyperbolic equations; one dimensional wave equations, two dimensional wave equation, one dimensional quasilineer hyperbolic equations Oral expression, Problem solving method.
10 Hyperbolic equations; one dimensional wave equations, two dimensional wave equation, one dimensional quasilineer hyperbolic equations Oral expression, Problem solving method.
11 Elliptic equations; Laplace equation, error analysis using maximum pyramid. Oral expression, Problem solving method.
12 Elliptic equations; Laplace equation, error analysis using maximum pyramid. Oral expression, Problem solving method.
13 Solution of difference equations; Newton and quasi Newton, direct methods, iteration methods (Thomas algorithm). Oral expression, Problem solving method.
14 finite volume method, finite element method, scattering methods. Multi-grid techniques. Oral expression, Problem solving method.
15 Finite element method, scattering methods. Oral expression, Problem solving method.
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