# MA202

## NUMERICAL METHODS

Solution of linear system - Gaussian elimination and Gauss-Jordan methods - LU - decomposition methods - Crout's method - Doolittle method - Cholesky'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 -Order of convergence of these methods - Horner's method - Graeffe's method - Birge-Vieta method - Bairstow's method.

Curve fitting - Method of least squares and group averages – Least - square approximation of functions - solution of linear difference equations with constant coefficients.

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.

REFERENCES:

1. Kandasamy, P.,Thilagavathy ,K.,and Gunavathy,S.,`Numerical Methods', Chand and Co.,2007.

2. Jain, M.K., Iyengar,S.R.,and Jain,R.K.,`Numerical Methods for Scientific and Engineering Computation', Wiley Eastern,1992.

3. Gerald,C.F., and Wheatley, P.O.,'Applied Numerical Analysis', M/s. Addison Wesley, 1994.