Information Package / Course Catalogue
Numerical Solution of Differential and Integral Equations
Course Code: MTK616
Course Type: Area Elective
Couse Group: Third Cycle (Doctorate Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 8
Objectives of the Course

To provide a unified account of numerical methods for solving integral, differential and partial differantial equations.

Course Content

The general approach to finding a solution to a differential equation (or a set of differential equations) is to begin the solution at the value of the independent variable for which the solution is equal to the initial values. One then proceeds in a step by step manner to change the independent variable and move across the required range.

Name of Lecturer(s)
Learning Outcomes
1.To develops skills in mathematics and computing in demand by industry
2.To solve problems and analize data in industry and commerce, such as biology (genomic research, medical imaging), engineering (computational mechanics), and digital libraries (indexing and searching vast corpuses of data).
3.To be able to define some mathematical concepts which are essential in his/her field
4.To be able to gain the skill of interpreting some interrelations among these concepts
5.To be able to use mathematical concepts in solving certain types of problems
Recommended or Required Reading
Weekly Detailed Course Contents
Week 1 - Theoretical
Discrete methods for solving ODEs: Review of Runge-Kutta methods, linear multistep methods (Adams) convergence and order
Week 2 - Theoretical
Review of Runge-Kutta methods, linear multistep methods (Adams) convergence and order.
Week 3 - Theoretical
A number of practical ODE/PDE problems from different areas of applications will be introduced. Implicit Runge-Kutta methods.
Week 4 - Theoretical
Stability regions, A-stability and other stability concepts. The BDF methods. Finite difference methods for linear equations and for more general problems.
Week 5 - Theoretical
The BDF methods. Finite difference methods for linear equations and for more general problems.
Week 6 - Theoretical
Implicit Runge-Kutta methods, deferred correction. Numerical solution of integral equations using different numerical methods.
Week 7 - Theoretical
Numerical solution of integral equations using different numerical methods.
Week 8 - Theoretical
Finite difference methods for heat equation, wave equation and Poisson's equation: The 5-point Formula, Midterm
Week 9 - Theoretical
Finite difference methods for heat equation, wave equation and Poisson's equation: The 5-point Formula
Week 10 - Theoretical
Numerical solution of parabolic Volterra-integro differential equations using Backward-Euler methods
Week 11 - Theoretical
Second order Numerical solution of parabolic Volterra-integro differential equations using CN methods
Week 12 - Theoretical
Numerical solution of hyperbolic Volterra-integro differential equations
Week 13 - Theoretical
Numerical solution of hyperbolic Volterra integral equations using Finite difference methods
Week 14 - Theoretical
Numerical error analysis
Week 15 - Final Exam
Final exam
Assessment Methods and Criteria
Type of AssessmentCountPercent
Assignment1%5
Term Assignment1%5
Midterm Examination1%20
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140342
Assignment1066
Term Project1066
Individual Work140570
Midterm Examination130232
Final Examination142244
TOTAL WORKLOAD (hours)200
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
OÇ-1
3
3
3
3
3
4
4
2
4
OÇ-2
4
4
4
4
4
4
4
2
2
5
OÇ-3
4
4
4
4
4
2
2
2
OÇ-4
4
4
4
4
4
3
3
OÇ-5
4
4
4
4
4
3
3
4
Adnan Menderes University - Information Package / Course Catalogue
2026