Contents
Error analysis: Introduction, floating points, errors, types of errors.
Solution of non-linear equation: Bisection method, Regula-Falsi method, Newton-Raphson method, Fixed-Point iterative method.
Solution of linear algebraic equation: Iterative methds: Jaccobi’s method, Guass-Seidal method.
Eigen values and Eigen vectors: Power method.
Interpolation and extrapolation: Differences: Forward, backward, central, operators and their relations. Newton’s forward interpolation formula. Newton’s backward interpolation formula, Newton’s divided difference formula, Lagrange’s interpolation formula. Stirling’s formula.
Numerical differentiation: Newton’s forward and backward differentiation formulae.
Numerical quadrature: Trapezoidal rule, Simpson’s one-third rule, Simpson’s three-eighth rule, Weddle’s rule, Gaussian quadrature.
Numerical solution of ordinary differential equations: Taylor series method, Euler’s and its modified methods, Runge-Kutta methods, Predictor Corrector Methods; Miline’s method, Adam-Bashforth method.
