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You are here:Open notes-->Anna-University-->MA2264-NUMERICAL-METHODS

**MA2264 NUMERICAL METHODS**

# How to study this subject

**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.31

**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:

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.

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.

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.

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.

**UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS 9+3**

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 - GaussSeidel

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+3

Lagrangian Polynomials – Divided differences – Interpolating with a cubic spline – Newton’s

forward and backward difference formulas.

**UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION 9+3**

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+3

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+3**

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.

TOTAL (L:45+T:15): 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 Edition, Printice

Hall of India Private Ltd, New Delhi, 2007.32

**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”, 6th

Edition, Khanna Publishers, New Delhi, 2004.

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