SYLLABUS FOR SEMESTER - IV (NM)

09MA401                        NUMERICAL METHODS                   

                                                                                                                             

OBJECTIVE:        

• 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.
• At the end of the course, the students would be acquainted with the basic concepts in numerical methods and their uses.

1. SOLUTION OF EQUATIONS                                                                            

Solutions of non linear equations by iteration method and Newton Raphson method-Solutions of linear system of equations by Gauss Elimination, Gauss Jordan, Gauss Jacobian and Gauss Seidal methods-Inverse of a matrix by Gauss Jordan.

2. INTERPOLATION AND APPROXIMATION                                                       

Equal Intervals-Newton’s Forward and Backward differences formulae-Unequal intervals-Newton’s divided differences formula and Lagrangian polynomials-Interpolating with cubic spline polynomial.

3. NUMERICAL DIFFERENTIATION AND INTEGRATION                                             

Newton’s Forward and Backward Differences to compute derivatives-Trapezoidal rule-Simpson’s 1/3 rule, Simpson’s 3/8 rule –Two and three point Gaussian quadrature formulas.

4. INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS       

Taylor series method-Euler and modified Euler method-Fourth order Runge-Kutta method for solving first order equations. Milne’s and Adam’s predictor and corrector methods.

5. BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL  EQUATIONS                                                                                                          

Finite difference solution of second order ordinary differential equations-Finite difference solutions of one dimensional heat equation by explicit and implicit methods-One dimensional wave equation and two dimensional Laplace and Poisson equations.

TEXT BOOKS

1. Venkataraman, M.K, “Numerical Methods”, National Publishing Company, 2000.
2. Kandasamy P, Thilagavathy,K, Gunavathi,K, “Numerical Methods”, S.Chand and   Co., New Delhi, 2005.

REFERENCE BOOKS

       1.   Veerarajan T, “Numerical methods: with Programs in C”, Tata McGraw Hill, New Delhi,

             2006. 

       2.   Jain M.K, Iyengar,K  and Jain R.K, “Numerical Methods for Scientific and Engineering  Computation”, New Age International (P) Ltd, Publishers, 2003.