MA 2264 - NUMERICAL METHODS |
UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS |
Solution of equation - Fixed point iteration: x=g(x) method – Newton’s method –
Solution of linear system by Gaussian elimination and Gauss-Jordon methods - Iterative
methods - Gauss-Seidel methods - Inverse of a matrix by Gauss Jordon method –
Eigen value of a matrix by power method and by Jacobi method for symmetric matrix |
UNIT II INTERPOLATION AND APPROXIMATION |
Lagrangian Polynomials – Divided differences – Interpolating with a cubic spline –
Newton’s forward and backward difference formulas. |
UNIT IIINUMERICAL DIFFERENTIATION AND INTEGRATION |
Differentiation using interpolation formulae –Numerical integration by trapezoidal and
Simpson’s 1/3 and 3/8 rules – Romberg’s method – Two and Three point Gaussian
quadrature formulas – Double integrals using trapezoidal and Simpsons’s rules. |
UNIT IVINITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL
EQUATIONS |
Single step methods: Taylor series method – Euler methods for First order Runge –
Kutta method for solving first and second order equations – Multistep methods: Milne’s
and Adam’s predictor and corrector methods. |
UNIT VBOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL
DIFFERENTIAL EQUATIONS |
Finite difference solution of second order ordinary differential equation – Finite difference
solution of one dimensional heat equation by explicit and implicit methods – One
dimensional wave equation and two dimensional Laplace and Poisson equations. |
Text Book |
1. VEERARJAN,T and RAMACHANDRAN.T, ‘NUMERICAL MEHODS with
programming in ‘C’ Second Edition Tata McGraw Hill Pub.Co.Ltd, First reprint
2007.
2. SANKAR RAO K’ NUMERICAL METHODS FOR SCIENTISITS AND
ENGINEERS –3rd Edition Princtice Hall of India Private, New Delhi, 2007. |
References |
1. P. Kandasamy, K. Thilagavathy and K. Gunavathy, ‘Numerical Methods’,
S.Chand Co. Ltd., New Delhi, 2003.
2. GERALD C.F. and WHEATE, P.O. ‘APPLIED NUMERICAL ANALYSIS’…
Edition, Pearson Education Asia, New Delhi. |