MA6459 Numerical Methods -Semester IV-AERO-BE-Anna University

ma6459-numerical-methods-semester-iv-aero-be-anna-universityMA6459 Numerical Methods -Semester IV-AERO-BE-Anna University AERO SEM IV Syllabus, AERO SYLLABUS

 

 

 

 

 

MA6459                                         NUMERICAL  METHODS                                                  L  T  P  C

3 1  0   4

OBJECTIVES

• This course aims at providing the necessary basic concepts of a few numerical methods and give procedures for solving numerically different kinds of problems occurring in engineering and technology

 

UNIT I             SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS                             10+3

Solution of algebraic and transcendental equations - Fixed point iteration method – Newton Raphson method- Solution of linear system of equations - Gauss elimination method – Pivoting - Gauss Jordan method – Iterative methods of Gauss Jacobi and Gauss Seidel - Matrix Inversion by Gauss Jordan method - Eigenvalues of a matrix by Power method.

 

UNIT II            INTERPOLATION  AND  APPROXIMATION                                                             8+3

Interpolation with unequal intervals - Lagrange's interpolation – Newton’s divided difference interpolation – Cubic Splines - Interpolation with equal intervals - Newton’s forward and backward difference formulae.

 

UNIT III           NUMERICAL  DIFFERENTIATION  AND  INTEGRATION                                        9+3

Approximation   of   derivatives   using   interpolation   polynomials   -   Numerical   integration   using Trapezoidal,  Simpson’s  1/3  rule  –  Romberg’s  method  -  Two  point  and  three  point  Gaussian quadrature formulae – Evaluation of double integrals by Trapezoidal and Simpson’s 1/3 rules.

 

UNIT IV           INITIAL  VALUE  PROBLEMS  FOR  ORDINARY  DIFFERENTIAL

EQUATIONS                                                                                                              9+3

Single Step methods - Taylor’s series method - Euler’s method - Modified Euler’s method - Fourth order Runge-Kutta method for solving first order equations - Multi step methods - Milne’s and Adams- Bashforth predictor corrector methods for solving first order equations.

 

UNIT V           BOUNDARY  VALUE  PROBLEMS IN ORDINARY  AND  PARTIAL

DIFFERENTIAL  EQUATIONS                                                                                   9+3

Finite difference methods for solving two-point linear boundary value problems - Finite difference techniques for the solution of two dimensional Laplace’s and Poisson’s equations on rectangular domain – One dimensional heat flow equation by explicit and implicit (Crank Nicholson) methods – One dimensional wave equation by explicit method.

 

 

OUTCOMES

 

TOTAL (L:45+T:15): 60 PERIODS

 

• The students will have a clear perception of the power of numerical techniques, ideas and would be able to demonstrate the applications of these techniques to problems drawn from industry, management and other engineering fields.

 

TEXT BOOKS

1. Grewal. B.S., and Grewal. J.S., " Numerical  methods  in  Engineering  and  Science", Khanna

Publishers, New Delhi, 9th Edition, 2007.

2. Gerald. C. F., and Wheatley. P. O., " Applied  Numerical  Analysis", Pearson Education, Asia, New Delhi, 6th Edition, 2006.

 

REFERENCES

1. Chapra.  S.C.,   and   Canale.R.P.,   "Numerical   Methods   for   Engineers,   5th     Edition,   Tata

McGraw - Hill, New Delhi, 2007.

2. Brian Bradie. "A friendly introduction to Numerical analysis", Pearson Education, Asia, New Delhi,

2007.

3. Sankara Rao. K., "Numerical methods for Scientists and Engineers", 3rd Edition, Prentice Hall of

India Private Ltd., New Delhi, 2007.