Computational Mathematics(MA608)

Course Name:

Computational Mathematics

Programme:

MCA

Semester:

Second

Category:

Programme Core (PC)

Credits (L-T-P):

(3-0-0) 3

Content:

Computer arithmetic - Floating point errors, Round-off errors, Absolute and relative errors; Polynomial interpolation: Lagrange and Newtons’s interpolation methods, Hermite interpolation; Curve fitting using least-square principle; Numerical differentiation through polynomial interpolation: Deduction of first and second order formulae; Numerical integration: Newton-Cotes formula, Trapezoidal and Simpson’s 1/3rd and 3/8th rules, Method of undetermined coefficients; Solution of linear system: Gauss-Elimination and LU-factorization, Basic iterative methods - a) Jacobi,

b) Gauss-Siedel, c) Successive over relaxation methods; Finding root of an equation: (polynomial and transcendental) - Bisection and Regula-falsi methods (bracketing roots), Newton- Raphson (Newton) method, fixed point iterations, Muller’s method; Extension of Newton’s method to nonlinear system of equations; Numerical solution of ODEs (IVPs): Euler’s and higher order Taylor series methods, Runge-Kutta methods, Predictor-Corrector methods: a) Modified Euler method, b) Linear multi-step methods.

References:

R L Burden and J D Faires, Numerical Analysis, 9 th Edn, Brooks/Cole.

S D Conte, C De Boor, Elementary Numerical Analysis, Tata McGraw-Hill, 2006

W H Press, S A Teukolsky, W T Vetterling, B P Flannery, Numerical Recipes in C/Fortran - The Art of Scientific Computing, Cambridge University Press, 2007.

M K Jain, S R K Iyengar, R K Jain, Numerical Methods for Scientific and Engineering Computation.