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MV 501 – COMPUTATIONAL METHODS
UNIT I – SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS:
Roots of equations – Newton – Raphson – Regula Falsi methods, solutions of linear systems – Gaussian, Gauss Jordan, Choleski, Jacobi, Gauss – Seidel methods, determination of eigen values – power – Jacobi - Givens methods.
UNIT II – CURVE FITTING AND INTERPOLATION :
Curve fitting – method of group averages – principle of least squares – method of moments, interpolation – Newton’s and Lagrange’s methods, Newton’s forward and backward difference formulae.
UNIT III – NUMERICAL DIFFERENTIATION AND INTEGRATION :
Numerical differentiation with interpolation polynomials – integration by trapezoidal and Simpson’s (1/3 and 3/8) rules – two and three point Gaussian quadiature formula – double integrals using trapezoidal and simpon’s rules – differentiation and integration of matrices.
UNIT IV – NUMERICAL SOLUTION OF ODE :
Single step methods – Taylor series – Euler and modified Euler – Rugekutta methods, multi step methods – Milne and Adam – Bashforth methods – Finite difference methods for second order differential equations.
UNIT V – NUMERICAL SOLUTION OF PDE :
Finite difference solution for one dimensional heat equation ( both implicit and explicit), one dimensional wave equation and two dimensional Laplace and Poisson equations – integral formulation for numerical solutions – variational – collocation – subdomain – Galerkins – least square methods, differentiation of matrix equations.
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| Author: Bala 14 Dec 2007 | Member Level: Diamond Points : 1 |
REFERENCE BOOKS :
1. Sastry.S.S. Introductory methods of Numerical Analysis, 3rd edition.
2. Grewal, B.S. and Grewal J.S. Numerical methods in Engineering and Science.
3. Jain, M.K. Iyengar, S.R.K. and Jain, R.K. Numerical methods for Engineering and Scientific computation, 3rd edition.
4. Chapra, S.C., and Canale. R.P. Numerical Methods for Engineers.
5. Gerald, C.F., and Wheatly.P.O., Applied Numerical Analysis.
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