Faculty of Science

Objectives

To introduce the fundamental concepts of numerical analysis with particular emphasis on numerical solution of ODE’s.

Contents

Numerical differentiation (the classical finite differences, compact finite differences, consistency and convergence analysis); Interpolation of functions (polynomial interpolation, splines and B-splines interpolation); Numerical integration (quadrature formulas, Newton’s cotes, Hermite quadrature formula, Richardson extrapolation, n-dimensional numerical integration, the Monte Carlo method); Approximation of functions with orthogonal polynomials (Fourier series, Chebyshev polynomials, Legendre polynomials, Gauss integration and interpolation, Chebyshev integration and interpolation, Legendre integration and interpolation, least square approximation); Numerical solution of ODE’s (the Cauchy problem, one step methods and convergence analysis, difference equations, multistep methods, consistence, stability and convergence analysis, Runnge-Kutta method); Systems of ODE’s.