MA2264 NUMERICAL METHODS

MA2264 NUMERICAL METHODS MA 2264 NUMERICAL METHODS

MA2264 NUMERICAL METHODS 3 1 0 4

(Common to Civil, Aero & EEE) (VISIT )

AIM

With the present development of the computer technology, it is necessary to develop

efficient algorithms for solving problems in science, engineering and technology. This

course gives a complete procedure for solving different kinds of problems occur in

engineering numerically.

OBJECTIVES

At the end of the course, the students would be acquainted with the basic

concepts in numerical methods and their uses are summarized as follows:

i. The roots of nonlinear (algebraic or transcendental) equations, solutions of large

system of linear equations and eigen value problem of a matrix can be obtained

numerically where analytical methods fail to give solution.

ii. When huge amounts of experimental data are involved, the methods discussed on

interpolation will be useful in constructing approximate polynomial to represent the

data and to find the intermediate values.

iii. The numerical differentiation and integration find application when the function in

the analytical form is too complicated or the huge amounts of data are given such

as series of measurements, observations or some other empirical information.

iv. Since many physical laws are couched in terms of rate of change of one/two or

more independent variables, most of the engineering problems are characterized in

the form of either nonlinear ordinary differential equations or partial differential

equations. The methods introduced in the solution of ordinary differential equations

and partial differential equations will be useful in attempting any engineering

problem.

1. 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 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.

2. INTERPOLATION AND APPROXIMATION 9

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

Newton’s forward and backward difference formulas.

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

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4. INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL

EQUATIONS 9

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.

5. 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

TEXT BOOKS

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.

REFERENCE BOOKS(VISIT )

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.