The Elimination method – Gauss Elimination method and Gauss Jordan method – LU Decomposition method Iterative methods –Gauss Seidal method and Gauss Jacobi method Solving Nonlinear Equations: Non linear systems.
Taylor series method – The Euler method and its modifications – Rungekutta methods –Multistep method – Milne’s method – Adams Moulton method.
The shooting method – solution through a set of equations – Derivative boundary conditions – Characteristic Value Problems: Eigen values of a matrix by Iteration – The power method.
Types of partial differential equations – Elliptic equations : Laplace Equation and Poisson equation – Solving for the temperature within the slab – Iterative method – Liebmann’s method.
Parabolic equations: Solving Heat equations– Crank Nicholson Method Hyperbolic Equations: Solving the vibrating string – Solving the wave equations in two dimensions.
Reference Book:
1. Numerical Methods for Engineers by S.C. Chapra and P.C. Raymond, 5 th Edition, Tata McGraw Hill,2007. 2. Numerical Analysis by R.L. Burden and J. Douglas Faires, P.W.S.Kent Publishing Company, Boston Fourth Edition,(1989). 3. Introductory methods of Numerical Analysis by S.S. Sastry, Prentice Hall of India, New Delhi, (1998).
Text Book:
APPLIED NUMERICAL ANALYSIS’ by C.F.Gerald and P.O.Wheatley, Seventh Edition, Addison Wesley, (2004). Unit I: Chapter 2 (sec 2.2, 2.5) and Chapter 1 (sec 1.7). Unit II: Chapter 6 (sec 6.1, 6.2, 6.3, 6.4). Unit III: Chapter 6 (sec 6.7, 6.8). Unit IV: Chapter 8 (sec 8.1). Unit V: Chapter 8 (sec 8.2, 8.3).
