MA51 NUMERICAL METHODS

MA51                                                             NUMERICAL METHODS                                     3 0 0 3

1. SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS

Solution of equation –Fixed point iteration – Newton Raphson method – Solution of linear system by Gaussian elimination and Gauss-Jordon method– Iterative method - Gauss-Seidel method - Inverse of a matrix by Gauss Jordon method – Eigen value of a matrix by power method and by Jacobi method for symmetric matrix.

2. INTERPOLATION AND APPROXIMATION

Gauss Forward and Backward difference formulae - Lagrangian Polynomials – Divided differences – Interpolating with a cubic spline – Newton’s forward and backward difference formulas.

3. NUMERICAL 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 formulae – Double integrals using trapezoidal and Simpsons’s rules.

4. INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

Single step methods: Taylor series method – Euler method for first order equation – Euler’s modified and improved methods for first order equation – Fourth order Runge – Kutta method for solving first and second order equations – Multistep methods: Milne’s and Adam’s predictor and corrector methods.

5. BOUNDARY 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.

L = 45 T = 15 Total = 60

TEXT BOOKS

1. Veerarjan, T and Ramachandran, T. ‘Numerical methods with programming in ‘C’ Second Editiion, Tata McGraw-Hill Publishing.Co.Ltd. (2007).

2. Sankara Rao K, ‘Numerical Methods for Scientisits and Engineers’ – 3rd edition Printice Hall of India Private Ltd, New Delhi, (2007).

REFERENCE BOOKS

1. Chapra, S. C and Canale, R. P. “Numerical Methods for Engineers”, 5th Edition, Tata McGraw-Hill, New Delhi, 2007.

2. Gerald, C. F. and Wheatley, P.O., “Applied Numerical Analysis”, 6th Edition, Pearson Education Asia, New Delhi, 2006.

3. Grewal, B.S. and Grewal,J.S., “ Numerical methods in Engineering and Science”, 6^th Edition, Khanna Publishers, New Delhi, 2004