Application Program for Numerical Integration

Cilj ovog rada bio je upoznavanje formula i algoritama za numerički izračun integrala te implementacija istih unutar aplikacije s grafičkim korisničkim sučeljem. Proučene su sljedeće metode: trapezna i Simpsonova formula te Rombergov i Gaussov algoritam. Sve metode su matematički izvedene, ostvarene programskim jezikom Java. Najvažniji isječci izvornog koda su prikazani u radu kao i rad same aplikacije na primjerima. Tako je jedan od primjera aproksimacija broja ln(2) svakom pojedinom metodom te primjer aproksimacije broja pi Rombergovim i Gaussovim algoritmom. Čitatelj pregledom umetnutih prikaza sučelja aplikacije može samostalno usporediti preciznosti pojedinih metoda.The aim of this paper was to familiarize the formulas and algorithms for the numerical calculation of integrals and their implementation within the application with the graphical user interface. The following methods were studied: Trapezoidal rule, Simpson's rule, Romberg's method and Gaussian quadrature. All the methods are mathematically derived, implemented using Java programming language. The most important source code snippets are shown in the work as well as the application work itself in the examples. So one of the examples was approximation of the ln(2) by each particular method and the example approximating pi by Romberg's and Gaussian algorithm. The reader can recognize precision of each method by comparing the values from the application screenshots