MA202

NUMERICAL TECHNIQUES

• 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.
• 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.
• Newton’s forward, backward and divided difference interpolation – Lagrange’s interpolation – Numerical Differentiation and Integration – Trapezoidal rule – Simpson’s 1/3 and 3/8 rules - Curve fitting - Method of least squares and group averages.
• 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 Adams’ methods.
• 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.

Books:

• Gerald, C.F. & Wheatley, P.O., Applied Numerical Analysis,Addison Wesley.
• Jain, M.K., Iyengar, S.R. & Jain, R.K., Numerical Methods for Scientific and Engineering Computation,Wiley Eastern.
• Kandasamy, P., Thilagavathy, K., & Gunavathy, S., Numerical Methods, Chand and Company.