MA6459 SYLLABUS NUMERICAL METHODS REGULATION 2013 ANNA UNIVERSITY

MA6459 SYLLABUS NUMERICAL METHODS REGULATION 2013 ANNA UNIVERSITY for students.

OBJECTIVES of MA6459 SYLLABUS :

This course aims at providing the necessary basic concepts of a few numerical methods and give procedures for solving numerically different kinds of problems occurring in engineering and technology

MA6459 SYLLABUS UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS

Solution of algebraic and transcendental equations – Fixed point iteration method – Newton Raphson method- Solution of linear system of equations – Gauss elimination method – Pivoting – Gauss Jordan method – Iterative methods of Gauss Jacobi and Gauss Seidel – Matrix Inversion by Gauss Jordan method – Eigen values of a matrix by Power method.

MA6459 SYLLABUS UNIT II INTERPOLATION AND APPROXIMATION

Interpolation with unequal intervals – Lagrange’s interpolation – Newton‟s divided difference interpolation – Cubic Splines – Interpolation with equal intervals – Newton‟s forward and backward difference formulae.

MA6459 UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION

Approximation of derivatives using interpolation polynomials – Numerical integration using Trapezoidal, Simpson‟s 1/3 rule – Romberg‟s method – Two point and three point Gaussian quadrature formulae – Evaluation of double integrals by Trapezoidal and Simpson‟s 1/3 rules.

MA6459 SYLLABUS UNIT IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

Single Step methods – Taylor‟s series method – Euler‟s method – Modified Euler‟s method – Fourth order Runge-Kutta method for solving first order equations – Multi step methods – Milne‟s and Adams-Bash forth predictor corrector methods for solving first order equations.

MA6459 UNIT V BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS

Finite difference methods for solving two-point linear boundary value problems – Finite difference techniques for the solution of two dimensional Laplace‟s and Poisson‟s equations on rectangular domain – One dimensional heat flow equation by explicit and implicit (Crank Nicholson) methods – One dimensional wave equation by explicit method.