MA2264 NUMERICAL METHODS

MA2264 NUMERICAL METHODS L T P C
3 1 0 4
UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS 9
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.
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UNIT II INTERPOLATION AND APPROXIMATION 9
Lagrangian Polynomials – Divided differences – Interpolating with a cubic spline –
Newton’s forward and backward difference formulas.
UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION 9
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.
UNIT IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL
EQUATIONS 9
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.
UNIT V BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL
DIFFERENTIAL EQUATIONS 9
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.
L : 45 , T : 15 ,TOTAL = 60 PERIODS
TEXT BOOKS:
1. Veerarajan, T and Ramachandran, T. ‘Numerical methods with programming in ‘C’
Second Editiion, Tata McGraw-Hill Publishing.Co.Ltd. (2007).
2. Sankara Rao K, ‘Numerical Methods for Scientisits and Engineers’ – 3rd editiion
Printice Hall of India Private Ltd, New Delhi, (2007).
REFERENCES:
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. Grewal, B.S. and Grewal,J.S., “ Numerical methods in Engineering and Science”,
6th Edition, Khanna Publishers, New Delhi, 2004
CS2021