MA 251: Numerical Methods

Credits: 3:0

Numerical solution of algebraic and transcendental equations, Iterative algorithms, Convergence, Newton Raphson procedure, Solutions of polynomial and simultaneous linear equations, Gauss method, Relaxation procedure, Error estimates, Numerical integration, Euler-Maclaurin formula. Newton-Cotes formulae, Error estimates, Gaussian quadratures, Extensions to multiple integrals.

Numerical integration of ordinary differential equations: Methods of Euler, Adams, Runge-Kutta and predictor - corrector procedures, Stability of solution. Solution of stiff equations.

Solution of boundary value problems: Shooting method with least square convergence criterion, Quasilinearization method, Parametric differentiation technique and invariant imbedding technique.

Solution of partial differential equations: Finite-difference techniques, Stability and convergence of the solution, Method of characteristics. Finite element and boundary element methods.  

Suggested books and references:

  1. Gupta, A. and Bose, S. C., Introduction to Numerical analysis, Academic Publishers, 1989.
  2. Conte, S. D. and Carl de Boor., Elementary Numerical Analysis, McGraw-Hill, 1980.
  3. Hildebrand, F. B., Introduction to Numerical Analysis, Tata McGraw-Hill, 1988.
  4. Froberg, C. E., Introduction to Numerical Analysis, Wiley, 1965.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 17 May 2024