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Anna University B.E. I&C - Sem 4 - NUMERICAL METHODS
Posted Date: 10 Dec 2007 Resource Type: Articles/Knowledge Sharing Category: General
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Posted By: Bala Member Level: Diamond
Rating:  Points: 1
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MA038 NUMERICAL METHODS
1. SOLUTION OF EQUATIONS AND EIGEN VALUE PROBLEMS
Iterative method, Newton – Raphson method for single variable and for simultaneous equations with two variables. Solutions of a linear system by Gaussian, Gauss-Jordan, Jacobi and Gauss – Seidel methods. Inverse of a matrix by Gauss – Jordan method. Eigen value of a matrix by Power and Jacobi methods.
2. INTERPOLATION Newton’s divided difference formulae, Lagrange’s and Hermite’s polynomials. Newton forward and backward difference formulae. Stirling’s and Bessel’s Central difference formulae.
3. NUMERICAL DIFFERENTIATION AND INTEGRATION
Numerical differentiation with interpolation polynomials, Numerical integration by Trapezoidal and Simpson’s (both 1/3rd and 3/8th) rules. Two and Three point Gaussian quadrature formula. Double integrals using Trapezoidal and Simpson’s rule.
4. INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS 9
Single step Methods – Taylor Series, Euler and Modified Euler, Runge – Kutta method of order four for first and second order differential equations. Multistep Methods-Milne and Adam’s Bashforth predictor and corrector methods.
5. BOUNDARY VALUE PROBLEMS FOR ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS 9
Finite difference solution for the second order ordinary differential equations. Finite difference solution for one dimensional heat equation (both implicit and explicit), One-dimensional wave equation and two-dimensional Laplace and Poisson equations.
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Responses
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| Author: Bala 10 Dec 2007 | Member Level: Diamond Points : 1 | TEXT BOOKS
1. Sastry, S.S., “Introductory Methods of Numerical Analysis (Third Edition)”, Prentice Hall of India, New Delhi, 1998.
REFERENCES
1. Kandasamy, P.,Thilakavthy, K. and Gunavathy, K. “Numerical Methods”, S.Chand and Co., New Delhi ,1999.
2. Grewal B.S., Grewal J.S., “Numerical Methods in Engineering and Science”, Khanna Publishers, New Delhi, 1999.
3. Jain M.K., Iyengar S.R.K and Jain R.K., “Numerical Methods for Engineering and Scientific Computation (Third Edition)”, New Age International (P) Ltd., New Delhi, 1995.
4. Gerald C.F., Wheatley P.O., Applied Numerical Analysis (Fifth Edition), Addison – Wesley, Singapore, 1998.
5. Narayanan S., Manickavachakam Pillai K. and Ramanaiah G., “Advanced Mathematics for Engineering Students-Vol.-III”, S.Viswanathan Pvt. Ltd., Chennai, 1993.
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