Numerical Methods for Engineering
Nuno Filipe Marcelino Martins
Weekly - 5
Total - Available soon
BURDEN, R.L.; FAIRES, J.D. (2011) -- Numerical Analysis (9th edition), Brooks/Cole, Boston, USA.
PINA, H. (1995) -- Métodos Numéricos, McGrawHill.
BRAUN, M. (1993) -- Differential Equations and their applications (4th edition). Springer-Verlag.
CIARLET, P.G. (1995) -- Introduction to Numerical Linear Algebra and Optimisation, Cambridge University Press, England.
I. Matrix numerical analysis:
1. Conditioning of matrices. Condition number.
2. Iterative methods for system of equations: Jacobi, Gauss-Seidel e Relaxação.
3. iterative methods for computing eigenvalues and eigenvectors: power iteration.
4. Rayleigh quotient.
II. Numerical solution of differential equations:
1. Euler, Taylor and Runge-Kutta methods.
2. Explicit and implicit multistep methods.
3. Predictor–corrector method (Adams--Bashforth e Adams – Moulton).
4. Finite difference methods for elliptic 1D problems (axial deformation of rods).
5. Finite difference methods of elliptic 2D problems (transverse deformation of membranes).
6. finite difference methods of 2D parabolic problems (head diffusion). Explicit, implicit and Crank—Nicolson algorithms.
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