1. SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS
- Solution of equation
Fixed point iteration: x=g(x) method - Newton’s method
- Solution of linear system
Gaussian elimination
Gauss-Jordon method
Iterative method
Gauss-Seidel method
- Inverse of a matrix by Gauss Jordon method
- Eigen value of a matrix
Power method
Jacobi method
2. INTERPOLATION AND APPROXIMATION
- Lagrangian Polynomials
- Divided differences
- Interpolating with a cubic spline
- Newton’s forward and backward difference formulas.
3. 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.
- 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.
5. BOUNDARY VALUE PROBLEMS IN ordinary AND PARTIAL DIFFERENTIAL
- wave equation
- Laplace quations.
- Poisson equations.
