Numerical Algorithms and Analysis(CMA707)

Course Name: 

Numerical Algorithms and Analysis

Programme: 

M.Tech (CMA)

Semester: 

Second

Category: 

Programme Core (PC)

Credits (L-T-P): 

(3-0-2)4

Content: 

Errors and Approximations: Order/Rate of convergence of an Iterative method-Solution of Algebraic, Transcendental and Polynomial equation-Newton-Raphson method, Extension of Newton-Raphson method for finding multiple roots and to solve system of non-linear equations. Mullers method, Chebyshev’s methods. Interpolation: Newton’s Divided difference method. Hermite’s interpolation. Cubic spline interpolation. Errors in interpolation. Numerical Differentiation: Finite difference operator techniques. Richardson’s extrapolation technique and differentiation of interpolating polynomials. Numerical Integration: Method of undetermined coefficients. Errors in integration formulae. Iterative solution of linear equations. Numerical solution of ordinary different equations: Initial value problems. Single step and multistep methods for solving first and second order Initial value problems. Solution of Boundary value problems by finite difference method and shooting method. Numerical solution of partial differential equations: Solution of elliptic partial differential equations by 5-point and 9-point schemes. Solution of hyperbolic partial differential equations by explicit and implicit schemes. Error Analysis

References: 

Jain M K, Iyengar S R K and Jain R K, Numerical Methods for Scientific and Engineering Computation, 4th Edn, New Age International Pvt Ltd (2005)
Jain M K, Numerical Solutions of Differential Equations, 2nd Edn, John Wiley and Sons Ltd (1984)
S S Sastry, Introductory Methods of Numerical Analysis, 5th Edn. Prentice Hall of India.

Department: 

Mathematical and Computational Sciences
 

Contact us

B R Shankar, Associate Professor and Head
Department of MACS, NITK, Surathkal
P. O. Srinivasnagar, Mangalore - 575 025
Karnataka, India.

  • Hot line: +91-0824-2474048

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