Package org.opensourcephysics.numerics

Class Integral

java.lang.Object
org.opensourcephysics.numerics.Integral
public final class Integral extends Object
Class Integral defines various integration algorithms. This class cannot be subclassed or instantiated because all methods are static.
Author:
Wolfgang Christian

  • Method Summary

    Modifier and Type
    Method
    Description
    static double[][]
    fillArray(Function f, double start, double stop, double tol, double[][] data)
    Fills the given data array with the intgral of the given function.
    static double[][]
    fillArray(Function f, double start, double stop, double tol, int n)
    Fills a data array with the integral of the given function.
    static double
    ode(Function f, double start, double stop, double tol)
    Computes the integral of the function using an ODE solver.
    static double
    romberg(Function f, double a, double b, int n, double tol)
    Integrates the function using Romberg's algorithm based on Richardson's deferred approach.
    static double
    simpson(double[] f, double h)
    Uses Simpson's rule to find the area of an array representing a function that's been evaluated at N intervals of size h, where N is an odd integer.
    static double
    simpson(Function f, double start, double stop, int n)
    Numerical integration using Simpson's rule.
    static double
    simpson(Function f, double start, double stop, int n, double tol)
    Numerical integration using Simpson's rule.
    static double
    trapezoidal(Function f, double start, double stop, int n, double tol)
    Integrates the function using the trapezoidal method.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Method Details

    • trapezoidal

      public static double trapezoidal(Function f, double start, double stop, int n, double tol)
      Integrates the function using the trapezoidal method.
      Parameters:
      f - the function
      start - the first ordinate.
      stop - the last ordinate.
      n - the number of partitions
      tol - relative tolerance
      Returns:
      the integral

    • simpson

      public static double simpson(Function f, double start, double stop, int n) throws IllegalArgumentException
      Numerical integration using Simpson's rule.
      Parameters:
      f - a function.
      start - the first ordinate.
      stop - the last ordinate.
      n - the number of partitions
      Returns:
      the integral
      Throws:
      IllegalArgumentException

    • simpson

      public static double simpson(Function f, double start, double stop, int n, double tol)
      Numerical integration using Simpson's rule.
      Parameters:
      f - the function
      start - the first ordinate.
      stop - the last ordinate.
      n - minimum number of partitions
      tol - relative tolerance
      Returns:
      the integral

    • romberg

      public static double romberg(Function f, double a, double b, int n, double tol)
      Integrates the function using Romberg's algorithm based on Richardson's deferred approach.
      Parameters:
      f - the function
      a -
      b -
      n -
      tol - tolerance
      Returns:
      the integral

    • simpson

      public static double simpson(double[] f, double h)
      Uses Simpson's rule to find the area of an array representing a function that's been evaluated at N intervals of size h, where N is an odd integer. Example of usage: int N=27; x=new double[N]; f=new double[N]; double a=0, b=5, h=(b-a)/(N-1); for (int i=0; i< N;i++){ x[i]=a+i*h; f[i]=x[i]*Math.exp(x[i]); } double sum=Simp.Simp(f,h); Results: sum=594.6615858178942

    • ode

      public static double ode(Function f, double start, double stop, double tol)
      Computes the integral of the function using an ODE solver.
      Parameters:
      f - the function
      start -
      stop -
      tol - relative tolerance
      Returns:
      the integral

    • fillArray

      public static double[][] fillArray(Function f, double start, double stop, double tol, int n)
      Fills a data array with the integral of the given function.
      Parameters:
      f - Function to be integrated
      start - double start of integral
      stop - double end of integral
      tol - double computation tolerance
      n - int number of data points
      Returns:
      double[][]

    • fillArray

      public static double[][] fillArray(Function f, double start, double stop, double tol, double[][] data)
      Fills the given data array with the intgral of the given function.
      Parameters:
      f - Function to be integrated
      start - double start of integral
      stop - double end of integral
      tol - double computation tolerance
      data - double[][]
      Returns:
      double[][]