# Numerical Solution of Differential Equations (MDES620) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Numerical Solution of Differential Equations MDES620 3 0 0 3 5
Pre-requisite Course(s)
MATH 276 Differential Equations Also good knowledge in computrer programming such as Fortran, C++ , MATLAB and MAPLE .
Course Language English N/A Ph.D. Face To Face Lecture. This course is designed to give engineering students in graduate level the expertise necessary to understand and use computational methods for the approximate/numerical solution of differential equations problems that arise in many different fields of science. The students who succeeded in this course; After successful completion of the course the student will be able to: 1-Choose an efficient method to solve the differential equation(s) coming from a certain application field, 2-Investigate the stability and convergence properties of the methods, 3-Recognize some of the numerical difficulties that can occur when solving problems arising in scientific applications. Numerical solution of initial value problems; Euler, multistep and Runge-Kutta methods; numerical solution of boundary value problems; shooting and finite difference methods; stability, convergence and accuracy; numerical solution of partial differential equations; finite difference methods for parabolic, hyperbolic and elliptic equations; explic

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Review to differential equations Read related sections in references
2 Numerical solutions of initial value problems; Euler, multistep and Runge-Kutta methods Read related sections in references
3 Numerical solutions of initial value problems; Euler, multistep and Runge-Kutta methods Read related sections in references
4 Numerical solutions of boundary value problems; Shooting and finite difference methods Read related sections in references
5 Numerical solutions of boundary value problems; Shooting and finite difference methods Read related sections in references
6 Stability, convergence and accuracy of the numerical techniques given Read related sections in references
7 Stability, convergence and accuracy of the numerical techniques given Read related sections in references
8 Partial differential equations and their solutions Read related sections in references
9 Numerical solution of partial differential equations; finite difference methods Read related sections in references
10 Numerical solution of partial differential equations; finite difference methods Read related sections in references
11 Numerical solution of parabolic, hyperbolic and elliptic equations by finite difference methods Read related sections in references
12 Explicit and implicit methods, Crank-Nicolson method Read related sections in references
13 Explicit and implicit methods, Crank-Nicolson method. System of ordinary differential equations Read related sections in references
14 Convergence, stability and consistency analysis of the methods Read related sections in references
15 Overall review -
16 Final exam -

### Sources

Course Book 1. Numerical Solution of Partial Differential Equations by K.W. Morton and D.F. Mayers, Cambridge University Press, 1994. 2. Numerical Analysis of Differential Equations by A. Iserles, Cambridge University Press, 1996. 3. Numerical Solution of Partial Differential Equations: Finite Difference Methods by G.D. Smith, Clarendon Press, Oxford, 1985. 4. Computer Methods for ODEs and Differential-Algebraic Equations by U.M. Ascher & L.R. Petzold, SIAM, 1998.

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 5 18
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 42
Final Exam/Final Jury 1 40
Toplam 8 100
 Percentage of Semester Work 60 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Ability to carry out advanced research activities, both individual and as a member of a team X
2 Ability to evaluate research topics and comment with scientific reasoning X
3 Ability to initiate and create new methodologies, implement them on novel research areas and topics X
4 Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions X
5 Ability to apply scientific philosophy on analysis, modelling and design of engineering systems X
6 Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level X
7 Contribute scientific and technological advancements on engineering domain of his/her interest area X
8 Contribute industrial and scientific advancements to improve the society through research activities X

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 16 5 80
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 10 50
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 15 30
Prepration of Final Exams/Final Jury