Introduction to numerical methods: Understanding sources of errors; round-off errors, truncation errors, floating point arithmetic, Convergence
Solution of linear systems: Gauss elimination, Gauss Jordan elimination, Gauss-Seidel method, Diagonal dominance, Banded matrices, storage schemes for banded matrices, skyline solver.
Solution of non-linear systems: Newton Raphson method, Local and global minimum, rates of convergence, convergence criteria, conjugate gradient method.
Ordinary Differential Equations: Taylor series, Euler method, Runge-Kutta method, Finite Difference Method
Partial Differential Equations: Finite Difference Method – Laplace equation, Poison equation, 1-D heat equation, 1-D wave equation. |
Text/Reference Books:
- S. D. Conte and C. de Boor, Elementary Numerical Analysis: An Algorithmic approach, 3rd edition, McGraw-Hill Book Company, New York, 1980
- D. Dahlquist, and Å.Björck, Translated by Ned Anderson, Numerical Methods, 1stedition, Dover Publication, New York,2003
- K. E. Atkinson, Introduction to Numerical Analysis, 2nd Edition, John Wiley,New York, 1989
- C. F. Gerald and P. O. Wheatley, Applied Numerical Analysis, 5th edition, Addison Wesley, Massachusetts, 1994
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