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.  

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Last updated: 22 Jun 2024