181401 NUMERICAL METHODS
(Common to Civil, Aero, Manu, EEE, ECE, CSE, IT, Chemical &Plastic)
SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS
Solution of equation –Fixed point iteration: x=g(x) method - Newton’s method – Solution of linear system by Gaussian elimination and Gauss-Jordon method– Iterative method - Gauss-Seidel method - Inverse of a matrix by Gauss Jordon method – Eigen value of a matrix by power method and by Jacobi method for symmetric matrix.
INTERPOLATION AND APPROXIMATION
Lagrangian Polynomials – Divided differences – Interpolating with a cubic spline –
’s forward and backward difference formulas. Newton
NUMERICAL DIFFERENTIATION AND INTEGRATION
Differentiation using interpolation formulae –Numerical integration by trapezoidal and Simpson’s 1/3 and 3/8 rules – Romberg’s method – Two and Three point Gaussian quadrature formulae – Double integrals using trapezoidal and Simpsons’s rules.
INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
Single step methods: Taylor series method – Euler method for first order equation – Fourth order Runge – Kutta method for solving first and second order equations – Multistep methods: Milne’s and Adam’s predictor and corrector methods.
BOUNDARY VALUE PROBLEMS IN ordinary AND PARTIAL DIFFERENTIAL EQUATIONS
Finite difference solution of second order ordinary differential equation – Finite difference
solution of one dimensional heat equation by explicit and implicit methods – One
dimensional wave equation and two dimensional Laplace and Poisson equations.
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2. Sankara Rao K, “Numerical Methods for Scientisits and Engineers”, 3rd Edition, Printice Hall of India Private Ltd,
, 2007. New Delhi
1. Chapra, S. C and Canale, R. P., “Numerical Methods for Engineers”, 5th Edition, Tata McGraw-Hill,
, 2007. New Delhi
2. Gerald, C. F. and Wheatley, P.O., “Applied Numerical Analysis”, 6th Edition, Pearson Education, Asia,
, 2006. New Delhi
3. Grewal, B.S. and Grewal,J.S., “ Numerical methods in Engineering and Science”, 6th Edition, Khanna Publishers,
, 2004. New Delhi