NUMERICAL TECHNIQUES

PRE-REQUISITE: Nil

Faculty: Dr. R.Ponalagusamy

OBJECTIVE: To find approximate solutions for complicated differential equations.

1. Solution of linear system - Gaussian elimination and Gauss-Jordan methods - LU - decomposition methods - Crout's method - Jacobi and Gauss-Seidel iterative methods - sufficient conditions for convergence - Power method to find the dominant eigenvalue and eigenvector.

2. Solution of nonlinear equation - Bisection method - Secant method - Regula falsi method - Newton- Raphson method for f(x) = 0 and for f(x,y) = 0, g(x,y) = 0 - Order of convergence - Horner's method - Graeffe's method - Bairstow's method.

3. NewtonÃƒÂ¯Ã‚Â¿Ã‚Â½s forward, backward and divided difference interpolation ÃƒÂ¯Ã‚Â¿Ã‚Â½ LagrangeÃƒÂ¯Ã‚Â¿Ã‚Â½s interpolation ÃƒÂ¯Ã‚Â¿Ã‚Â½ Numerical Differentiation and Integration ÃƒÂ¯Ã‚Â¿Ã‚Â½ Trapezoidal rule ÃƒÂ¯Ã‚Â¿Ã‚Â½ SimpsonÃƒÂ¯Ã‚Â¿Ã‚Â½s 1/3 and 3/8 rules - Curve fitting - Method of least squares and group averages.

4. Numerical Solution of Ordinary Differential Equations- Euler's method - Euler's modified method - Taylor's method and Runge-Kutta method for simultaneous equations and 2nd order equations - Multistep methods - Milne's and AdamsÃƒÂ¯Ã‚Â¿Ã‚Â½ methods.

5. Numerical solution of Laplace equation and Poisson equation by Liebmann's method - solution of one dimensional heat flow equation - Bender - Schmidt recurrence relation - Crank - Nicolson method - Solution of one dimensional wave equation.

TEXTBOOKS

1. Steven C. Chapra and Raymond P. Canale "Numerical Methods for Engineers", Tata McGraw Hill,1995.

2. S.S.Sastry, "Introductory methods of Numerical analysis". Prentice - Hall of India.

REFERENCES

1. Gerald, C.F., and Wheatley, P.O., Applied Numerical Analysis, Addison Wesley.

2. Jain, M.K., Iyengar, S.R. and Jain, R.K., Numerical Methods for Scientific and Engineering Computation, Wiley Eastern.

3. Kandasamy, P., Thilagavathy, K., and Gunavathy, S., Numerical Methods, Chand and Company.