MA 251: 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
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:
Gupta, A. and Bose, S. C., Introduction to Numerical analysis
,Academic Publishers, 1989.
Conte, S. D. and Carl de Boor., Elementary Numerical Analysis
Hildebrand, F. B., Introduction to Numerical Analysis
,Tata McGraw-Hill, 1988.
Froberg, C. E., Introduction to Numerical Analysis
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