NUMERICAL METHODS Syllabus

MA2264 NUMERICAL METHODS L T P C
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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.
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.
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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.
TEXT BOOKS:
L = 45 , TOTAL: 45 PERIODS
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