MA2264 NUMERICAL METHODS

MA2264 NUMERICAL METHODS
 

L T P C

3 1 0 4

UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS 9

Solution of equation –Fixed point iteration: x=g(x) method - Newton’s 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.

UNIT II INTERPOLATION AND APPROXIMATION 9

Lagrangian Polynomials – Divided differences – Interpolating with a cubic spline –

Newton’s forward and backward difference formulas.

UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION 9

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.

UNIT IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL

EQUATIONS 9

Single step methods: Taylor series method – Euler method 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.

UNIT V BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL

DIFFERENTIAL EQUATIONS 9

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 PERIODS

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 editiion

Printice Hall of India Private Ltd, New Delhi, (2007).

REFERENCES

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”, 6th

Edition, Khanna Publishers, New Delhi, 2004