## Thursday, March 14, 2013

### Numerical Methods Lecture Notes Anna University

University : Anna University

Subject     : MA2264 NUMERICAL METHODS

SEMESTER:Common To All Branches

UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS

Solution of equation –Fixed point iteration: x=g(x) method - Newton’s method – Solution of  linear system by Gaussian elimination and Gauss-Jordon method– Iterative method - GaussSeidel method - Inverse of a matrix by Gauss Jordon method – Eigen value of a matrix by  power method and by Jacobi method for symmetric matrix.

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

Differentiation using interpolation formulae –Numerical integration by trapezoidal and Simpson’s  1/3 and 3/8 rules – Romberg’s method – Two and Three point Gaussian quadrature formulae – Double integrals using trapezoidal and Simpsons’s rules.

UNIT IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

Single step methods: Taylor series method – Euler method for first order equation – Fourth  order Runge – Kutta method for solving first and second order 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.

Numerical Methods Anna University Subject Notes

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