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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 5050 ANALYSIS OF NUMERICAL METHODS FOR THE ORDINARY DIFFERENTIAL EQUATIONS ELECTIVE 3 0 0 6

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

Offered to

Mathematics Mathematics

Course Objective

This course shows how to derive, test and analyze numerical methods for solving ordinary differential equations. The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done

Learning Outcomes of the Course Unit

1   will be able to construct and implement numerical methods for numerical integration and differentiation, and the solution of nonlinear system of equations 2   will be able to explain mathematical ideas of numerical methods in solving ordinary differential equations; 3   will be able to construct one-step and linear multistep methods for the numerical solution of initial-value problems for ordinary differential equations 4   will be able to construct one-step and linear multistep methods for the numerical solution systems of such equations and analyze their stability and accuracy properties 5   will be able to implement numerical methods for solving initial and boundary value problems by software packages like Mathematica

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Introduction to ODEs: Existence and Uniqueness Theorem 2 Local description of one step methods, Explicit and Implicit Euler Method, Finite Taylor series methods 3 Runge-Kutta methods, Predictor-corrector method 4 Global description of one step methods, stability,convergence, asymptotics of global error 5 Error monitoring and step control, estimation of global error, truncation error estimates, step control 6 Stiff problems, A-stability, pade approximation, region of absolute stability 7 Local description of multi step methods, explicit and implicit methods 8 Midterm 9 Local accuracy of multistep methods, polynomial degree vs. order 10 Adams-bashforth method, adams-moulton method, predictor corrector methods 11 Global description of multistep methods, linear difference equations 12 Stability and root condition, convergence,asymptotic of global error, estimation of global error 13 Analytic theory of order and stability, analytic characterization of order, stable methods of maximum order 14 Stiff problems, A stability of multistep methods

Recomended or Required Reading

Walter Gautschi, Numerical Analysis, Springer, 2012 J.C.Butcher, Numerical Methods for Ordinary Differential Equations, Wiley, 2008 David F. Griffiths, Desmond J. Higham, Numerical Methods for Ordinary Differential Equations, Springer, 2010

Planned Learning Activities and Teaching Methods

Lecture notes Presentation Homeworks

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 ASG ASSIGNMENT 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE MTE * 0.20 + ASG * 0.40 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.20 + ASG * 0.40 + RST * 0.40 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

sennur.somali@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 3 39 Preparations before/after weekly lectures 13 3 39 Preparation for midterm exam 1 10 10 Preparing assignments 10 4 40 Preparation for final exam 1 15 15 Midterm 1 3 3 Final 1 3 3 TOTAL WORKLOAD (hours) 149

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 LO.1 5 5 5 5 5 5 5 4 3 5 4 LO.2 4 5 5 5 5 4 5 3 5 4 LO.3 4 5 5 5 5 5 4 4 3 5 4 LO.4 3 4 5 5 4 5 5 4 2 4 4 LO.5 3 4 5 5 4 5 5 4 2 4 4