# MA202

### NUMERICALTECHNIQUES

FACULTY MEMBER :

DEPARTMENT OF MATHEMATICS

OBJECTIVE :

To provide the idea of various computational methods; concepts, which have close application to the guide.

1. NON-LINEAR EQUATIONS:

Solving non linear equations-Regula Falsi method-Newton's method-order of convergence-Graeffe's method and Bairstow's methodincluding the case of pairs of complex roots-Newton's method for f(x,y)=0,g(x,y)=0.

2. LINEAR SYSTEMS:

Solution of linear equations-Gaussian elimination,Gauss Jordan and Crout's methods-Finding the inverse of a matrix using elementary row transformations-Gauss Seidel and Jacobi iterative methods-Power method to find dominant eigen value and eigen vector.

3. INTERPOLATION AND CURVE FITTING:

Newton's forward and backward interpolation-Lagrange's interpolation-Newton's divided difference method-cubic spline interpolation-natural splines-choosing appropriate curve and fitting to data-curve fitting-Method of least Squares-regression equations.

4. NUMERICAL SOLUTION OF ODE(Ordinary Differential Equation):

Euler's method-Euler's modified method-Taylor's method - Runge-Kutta method of second and fourth order-Simultaneous equations and higher order equations by Taylor's method and Runge-Kutta method-Multistep method-Milne's and Adams' predictor-corrector methods.

5. NUMERICAL SOLUTION OF PDE(Partial Differential Equation):

Boundary value problems - finite difference methods - second order linear PDEs - solution of Laplace and Poisson equation by Liebmann's method - solution of one Dimensional heat flow and wave equations.

TEXT BOOKS:

1. M. K. Venkataraman, "Numerical Methods in Science and Engineering" NPC 2nd Edn.,(For Unit I)1986.

2. M.K.Jain, SRK lyengar and R.K.Jain, "Numerical Methods for Scientific and Engineering Computation", Wiley Eastern, 1992.

REFERENCE:

1. C.F. Gerald, "Applied Numerical Analysis", 2nd Edn., Addison Wesley Publishing Company (For Unit I) 1978, 4th Edn., 1989.