Course detail
Numerical Methods II
FSI-3NUAcad. year: 2012/2013
The course is devoted to numerical methods for differential equations. The course deals with the following topics: numerical methods for initial value problems of ordinary differential equations. Numerical methods for solving boundary value problems in ordinary differential equations. Numerical methods for solving partial differential equations of elliptic, parabolic and hyperbolic type. The course is based on the problem-solving environment MATLAB.
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COURSE CLASSIFICATION: A (excellent): 100--90, B (very good): 89--80, C (good): 79--70, D (satisfactory): 69--60, E (sufficient): 59--50, F (failed): 49--0.
Course curriculum
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Specification of controlled education, way of implementation and compensation for absences
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Prerequisites and corequisites
Basic literature
LeVeque, R.J.: Finite Difference Methods for Ordinary and Partial Differential Equations. SIAM, Philadelphia, 2007.
Moler, C.B.: Numerical Computing with MATLAB, Siam, Philadelphia, 2004.
Shampine, L.F., Gladwell, S., Thompson, S.: Solving ODEs with MATLAB, Cambridge University Press, Cambridge, 2003.
Shampine, L.F.: Numerical Solution of Ordinary Differential Equations, Chapman & Hall, New York, 1994.
Versteeg, H.K., Malalasekera, W.: An Introduction to Computational Fluid Dynamics. Pearson Prentice Hall, Harlow, 2007.
Recommended reading
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Computer-assisted exercise
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Syllabus
2. Explicit Runge-Kutta methods, step size control, matlab functions ode23 and ode45.
3. Adams methods, predictor corrector technique, variable-step-variable-order approach, matlab function ode113.
4. Stiff initial value problems, backward differentiation methods, matlab function ode15s.
5. Solving selected initial value problems in MATLAB.
6. Boundary value problem for ODE, shooting method, matlab function bvp4c.
7. Boundary value problem for ODE, difference method, finite volume method.
8. Boundary value problem for ODE, finite element method.
9. Elliptic PDE2, difference method, finite element method.
10. Elliptic PDE2, finite element method - continuation.
11. Parabolic PDE2, methods of lines, matlab function pdepe.
12. Hyperbolic PDE2, methods of lines.
13. Hyperbolic PDE1, upwind technique.