Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate

SUBJECT

Code
Subject
ME046 Numerical Simulation Techniques Using MATLAB
Section
Semester
Hours: C+S+L
Category
Type
Computer Science - in Romanian
8
2+0+2
optional
Applied Mathematics
8
2+0+2
compulsory
Teaching Staff in Charge
Prof. TRIF Damian, Ph.D.,  dtrifmath.ubbcluj.ro
Aims
The course is aimed at those who are active in computer simulation or are planning to become so. In effect, the student will learn to couple his/her understanding of basic mathematics with numerical methods in order to obtain solutions to engineering problems.
Content
1. Practical problems, models,inverse problems
2. Automatic differentiation and interval arithmetic (INTLAB package)
3. Qualitative studies, singular points, bifurcations
4. Ill-conditionned problems, regularization
5. Shadowing and validation of numerical results
6. Chebfun, LiScM, accdot
References
Hairer E., Numerical Geometric Integration, Internet course, 1999, http://www.unige.ch/math/folks/hairer/polycop.html
Hargreaves G. I., Interval Analysis in MATLAB, Numerical Analysis Report No. 416, Univ. of Manchester, 2002, http://www.ma.man.ac.uk/~nareports
Lynch S., Dynamical Systems with Applications using MATLAB, Birkhäuser, 2004.
Morosanu Gh., Ecuatii diferentiale. Aplicatii, Ed. Academiei RSR, 1989.
Parker T. S., Chua L. O., Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag, 1989.
Stauning O., Automatic Validation of Numerical Solutions, IMM-PHD-1997-36, Thesis, Lyngby, 1997, http://citeseer.nj.nec.com/stauning97automatic.html
Trif D., Metode numerice in teoria sistemelor dinamice, Transilvania Press, 1997.
Watson H. A. Jr., Differential Equations for Reliability, Maintainability, and Availability, Internet course, 1997, http://mathforum.org/differential/watson/
Zeldovich Ya. B., Myškis A. D., Elements of Applied Mathematics, Mir Publishers Moskow, 1976.
Assessment
individual project 50%, final exam 50%
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject