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MV1301 COMPUTATIONAL METHODS
Posted Date: 25 Apr 2008 Resource Type: Articles/Knowledge Sharing Category: Syllabus
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Posted By: Nithya Krishna Member Level: Gold
Rating:  Points: 6
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MV1301 COMPUTATIONAL METHODS
UNIT I SOLUTION OF EQUATIONS AND EIGEN VALUE PROBLEMS
Roots of equations – Newton – Raphson – Regular 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 rules – two and three point Gaussian quadrature formula – double integrals using trapezoidal and Simpson’s rules – differentiation and integration of matrices.
UNIT IV NUMERICAL SOLUTION OF ODE
Single step methods – Taylor series – Euler and modified Euler – Rungekutta methods, multi step methods – Miller and Adam – Bash forth 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 – variation – collocation – sub domain – Galerkins – least square methods, differentiation of matrix equation.
TEXT BOOKS
1. Sastry.S.S. “Introductory methods of Numerical Analysis”, 3rd edition, Prentice – Hall of India (P) Ltd., India, 2002
2. Chapra, S.C., and Canale. R.P. “Numerical Methods for Engineers”, 4th Edition, Tata McGraw-Hill, New Delhi, 2002.
REFERENCES
1. Jain, M.K. Iyengar, S.R.K. and Jain, R.K. “Numerical methods for Engineering and Scientific computation, 3rd edition, New Age International (P) Ltd., New Delhi, 1993.
2. Gerald, C.F., and Wheatly.P.O., “Applied Numerical Analysis”, 5th Edition, Addision – Wesley, New York, 1998.
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