MA 9262 NUMERICAL METHODS

MA 9262 NUMERICAL METHODS

1. 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 methods – Iterative methods of Gauss-Jacobi and Gauss-Seidel - Matrix Inversion by Gauss-Jordan method - Eigenvalues of a matrix by Power method and by Jacobi’s method.

2. INTERPOLATION AND APPROXIMATION

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

3. NUMERICAL DIFFERENTATION AND INTEGRATION (9 + 3)

Approximation of derivatives using interpolation polynomials - Numerical integration using Trapezoidal, Simpson’s 1/3 and Simpson’s 3/8 rules – Romberg’s method - Two point and three point Gaussian quadrature formulae – Evaluation of double integrals by Trapezoidal and Simpson’s rules.

4. 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 and second order equations - Multi-step methods - Milne’s and Adams-Bashforth predictor-corrector methods for solving first order equations.

5. 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.

TEXT BOOKS

1. Grewal, B.S. and Grewal,J.S., “ Numerical methods in Engineering and Science”, 6th Edition, Khanna Publishers, New Delhi, 2004.

2. Sankara Rao, K. “Numerical methods for Scientists and Engineers’, 3rd Edition Prentice Hall of India Private Ltd., New Delhi, 2007.

REFERENCE BOOKS

1. Chapra, S. C and Canale, R. P. “Numerical Methods for Engineers”, 5th Edition, Tata McGraw-Hill, New Delhi, 2007.

2. Gerald, C. F. and Wheatley, P. O., “Applied Numerical Analysis”, 6th Edition, Pearson Education Asia, New Delhi, 2006.

3. Brian Bradie, “A friendly introduction to Numerical analysis”, Pearson Education Asia, New