MAT6018 Numerical Solutions of Differential Equations IIBahçeşehir UniversityDegree Programs MATHEMATICS (TURKISH, PHD)General Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
PhD TR-NQF-HE: Level 8 QF-EHEA: Third Cycle EQF-LLL: Level 8

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT6018 Numerical Solutions of Differential Equations II Spring 3 0 3 8
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Assoc. Prof. ERSİN ÖZUĞURLU
Recommended Optional Program Components: None
Course Objectives: To see the applications and numerical solution of the partial differential equations.

Learning Outcomes

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.

Course Content

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.

Weekly Detailed Course Contents

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 / Textbooks: 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

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Quizzes 5 % 15
Midterms 2 % 45
Final 1 % 40
Total % 100
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Study Hours Out of Class 14 5 70
Quizzes 5 5 25
Midterms 2 20 40
Final 1 23 23
Total Workload 200

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
Program Outcomes Level of Contribution