21MAT432 NUMERICAL METHODS-

Unit I-

Roots of Transcendental and Polynomial Equations: Bisection method, Iteration methods based on first degree equation, Rate of convergence, system of nonlinear equations, Solution of System of Linear Algebraic Equations: Iteration methods Eigenvalues and Eigenvectros: Jacobi Method for symmetric matrices, Power method for arbitrary matrices.

Unit II-

Interpolation and Approximation: Lagrange and Newton interpolation for unequal intervals, Finite difference operators, Interpolating polynomials using finite differences.

Unit III-

Differentiation and Integration: Numerical differentiation, Methods based on interpolation, Numerical integration, Methods based on undetermined coefficients.

Unit IV-

Solutions of Ordinary Differential Equations: Initial Value problems, single step methods, Taylor series method, Second, Third and Fourth order Runge-Kutta methods.

Unit V-

Solutions of Partial Differential equations: Elliptic partial Differential equations, Parabolic partial differential equations, Hyperbolic partial differential equations.

TEXTBOOKS:

1. M.K. Jain, S.R.K. Iyengar and R.K. Jain, Numerical methods for scientific and Engineering computation, New Age International Publishers, 2007, 5th edition.
2. R.L. Burden, J. D. Faires, Numerical Analysis, Richard Stratton, 2011, 9th edition.

REFERENCES:

1. S.D. Conte and Carl de Boor, ‘Elementary Numerical Analysis; An Algorithmic Approach’. International series in Pune and Applied Mathematics, McGraw Hill Book Co., 1980.
2. Kandasamy P, Thilagavathi.K and Gunavathi. K. ‘Numerical Methods’- S. Chand and Company Ltd., New Delhi- Revised Edition 2007.