Unit I. Understanding sources of errors; round-off errors, truncation errors, floating point arithmetic, Convergence, Gauss elimination, Gauss Jordan elimination, Gauss-Seidel method, Diagonal dominance, Banded matrices, storage schemes for banded matrices, skyline solver.
Unit II. Newton Raphson method, Local and global minimum, rates of convergence, convergence criteria, conjugate gradient method.
Unit III. Taylor series, Euler method, Runge-Kutta method, Finite Difference Method
Unit IV. Finite Difference Method – Laplace equation, Poison equation, 1-D heat equation, 1-D wave equation.
Text/Reference Books:
- J 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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