### MA 5470 Numerical Analysis

#### Course Details

Norms of vectors and matrices, liner systems: direct and iterative schemes, ill conditioning and convergence analysis; Numerical Schemes for non-linear systems, Regression, Numerical solution of differential equations: Single step and multi-step methods, order, consistency, stability and convergence analysis, stiff equtations, two point boundary value problems: Shooting and finite difference methods.

#### Course References:

Text Books:

1. David Kinciad & Ward Cheney, Numerical Analysis and mathematics of scientific Computing, Brooks/Cole,1999.

2. J D Lambert, Computational methods in ordinary differential equations, Wiley and Sons, 1973

.
3. J C Butcher, The numerical analysis of ordinary differential equations, John wiley, 1987.

References:

1. K.Atkinson, Elementary Numerical Analysis, Jhon Wiley,1978

2. Curtis E Gerald & Partrock O Whealtley, Applied Numerical Analysis, Addison Wesley, 1988.

3. M.K.Jain S.R.K.Iyengar, R.K.Jain, Numeric Methods for Scientific and Engineering, Computation, Wiley Eastern, 2003.

4. John H Mathews, Numerical Methods for Mathematics, Science and Engineering, Prentice Hall of India,1994.

5. K.Shankara Rao, Numerical Methods for Sceintists and Engineers, Prentice Hall of India, 2001.

6. L.N.Trefethen, Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, http://www.comlab.ox.ac.uk/nick.trefethen/pdetext.html, (unpublished text), 1996

7. A.Iserles, A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, 1996.