NUMERICAL METHODS

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.

Books

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

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 31 May 2023
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