Metody numerické integrace s podrobnějším zaměřením na Rombergovu metodu

Abstract

It is often too difficult to calculate a given definite integral only by means of mathematical analysis, therefore, we have to use proper numerical approaches. Approximation of definite integrals are generally based on cutting a given interval into subintervals and on each of them we approximate the function by a polynomial. The very basic methods of numerical integration converge only very slowly, to accelerate the convergence we can use, i.e, Gaussian quadrature or Romberg's method. The latter is based on the so-called Richardson extrapolation and it uses composite integration schemes on gradually refined grids to improve the rate of convergence.