org.opensourcephysics.numerics
Class Integral

java.lang.Object
  org.opensourcephysics.numerics.Integral

public final class Integral
extends java.lang.Object

Class Integral defines various integration algorithms. This class cannot be subclassed or instantiated because all methods are static.

Author:

Wolfgang Christian

Method Summary

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 Detail

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 java.lang.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:

java.lang.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[][]