Jun 30, 2013 - 2.4.1 Second order RungeâKutta methods . . . . . . . . . . . 38 .... calculator or a computer algebra system to solve some problems numerically ...... The method (2.156) is a two-stage, fourth order implicit RungeâKutta method.
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Numerical Methods for Computer Engineering Mitchai Chongcheawchamnan
Picture description : Numerical simulation of side wind effects on a high-speed train (German Aerospace Center ; website: www.dlr.de)
Syllabus • Mathematic modeling and engineering problem solving • Introduction to software used for problem solving (SCILAB;MATLAB) • Approximation (Round-off errors, accuracy and precision, truncation errors, Taylor series, application of Taylor series for approximation problems ) • Numerical differentiation and integration • Error propagation • Graphical methods for root estimation Picture description : Airflow around the Hypersonic Vehicle JAPHAR (The French Aerospace Lab. ; website: www.onera.fr)
Syllabus (contd.) • Bisection method, Bracketing method, Fixedpoint iteration method, Secant method • Roots of polynomial estimation • Solving linear equation system • Solving nonlinear equation system using fixedpoint iteration method • The Newton-Raphson method • Some examples of root estimation in engineering applications • Optimization • Curve fitting Picture description : Airflow around the Hypersonic Vehicle JAPHAR (The French Aerospace Lab. ; website: www.onera.fr)
Marking plan • • • •
Class attending + others Assignment Midterm Examination Final Examination
10% 35% 25% 30%
Software as a teaching tool • MATLAB • SciLAB
References [1] S. C. Chapra and R. P. Canale, Numerical Methods for Engineers with Software and Programming Applications (International edition), 4th ed.,McGraw-Hill Higher Education, 2002. [2] S. L. Campbell, J-P Chancelier and R. Nikoukhah, Modeling and Simulation in Scilab/Scicos, Springer Science and Business Media, Inc, 2006. [3] S.C Chapra, Applied Numerical Methods with MATLAB, McGrawHill, 2nd, 2008. [4] Scilab Group, Introduction to SciLAB : Users’s Guide. [5] Mathworks, MATLAB Users’s Guide
Example movies Numerical simulation of a supersonic hotjet (Top: Temperature, Buttom : Pressure)