MA1351 – NUMERICAL METHODS
UNIT I
SOLUTION OF EQUATIONS AND EIGEN VALUE PROBLEMS
Linear interpolation methods (Method of False Position) − Newton’s method −Statement of fixed point theorem − Fixed point iteration: x=G(x) method − Solution of linear system by Gaussian elimination and Gauss-Jordon methods − Iterative Methods: Gauss Jacobi and Gauss-Seidel Methods − Inverse of a matrix by Gauss Jordon Method – Eigen value of a matrix by power method.UNIT II
INTERPOLATION AND APPROXIMATION
Lagrangian polynomials − Divided differences − Interpolating with a Cubic Spline − Newton’s Forward and backward difference formulas.
UNIT III
NUMERICAL DIFFERENTIATION AND INTEGRATION
Derivatives from difference tables divided differences and finite differences −
Numerical integration by trapezoidal and simpson’s 1/3 and 3/8 rules − Romberg’s
method − Two and three point Gaussian quadrature formulas − Double integrals using
trapezoidal and Simpson’s rules.
method − Two and three point Gaussian quadrature formulas − Double integrals using
trapezoidal and Simpson’s rules.
UNIT IV
INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
Single step methods: Taylor series method − Euler and modified Euler methods − Fourth order runge − Kutta method for solving first and second order differential equations − Multistep Methods: Milne’s and Adam’s predictor and corrector methods.
UNIT V
BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
Finite difference solution of second order ordinary differential equation − Finite difference solution of one dimensional heat equation by explicit and implicit methods − One dimensional wave equation and two dimensional Laplace and Poisson equations.
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