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Boudreau and Swanson: Applied Computational Physics

Chapter 05: Numerical Quadrature

example code (.tgz)

  • SIMPLEINTEGRATOR: illustrates the use of the SimpleIntegrator class to apply the trapezoid rule.
  • ROMBERGINTEGRATOR: illustrates the use of the RombergIntegrator class.
  • PLOTORDEROFCONVERGENCE: integrates several functions and plots the error as a function of the mesh spacing on a log-log plot.
  • TCHEBY: plots a Tchebyshev polynomial together with its roots using an analytic formula that happens to exist for these polynomials. The program takes command line arguments:
    ../local/bin/tcheby N=val Type=type[1/2]
    where N is the degree of the polynomial.
  • LAGUERRE: plots a Laguerre polynomial together with its roots using the three-term recurrence relation. The program takes command line arguments:
    ../local/bin/laguerre n=val a=val where n is the degree and a is the order of the polynomial.
  • COMPALG: compares the performance of various integration algorithms applied to a simple smooth function.
  • GAUSS: applies Gauss-Legendre integration to the normal distribution, integrating it on the interval [-1,1]. A single command line argument (an integer) determines the number of points used in the integration.

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