MA2264 Numerical Methods - SUBJECT CATALOG

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SYLLABUS:

MA2264                      NUMERICAL METHODS     L T  P  C 

                            (Common to Civil, Aero & EEE) 3  1 0  4

AIM

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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 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.

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 formulas – 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 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.

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 Edition  Tata McGraw Hill Pub.Co.Ltd, First reprint 2007.

2.  SANKAR RAO K’ NUMERICAL METHODS FOR SCIENTISTS AND ENGINEERS –3rd  Edition

Princtice Hall of India Private, New Delhi, 2007.

REFERENCES

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.