com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution

Class MixedRule

java.lang.Object

com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.DoubleExponential

com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.MixedRule

All Implemented Interfaces:

SubstitutionRule, java.io.Serializable

public class MixedRule
extends DoubleExponential

The mixed rule is good for functions that fall off rapidly at infinity, e.g., \(e^{x^2}\) or \(e^x\) The integral region is \((0, +\infty)\). The tricky part of using this transformation is to figure out a good range for t. If there is information about the integrand available, SubstitutionRule.ta() and SubstitutionRule.tb() should be overridden. The substitution is \[ x = e^{t - e^{-t}} \]

See Also:

Wikipedia: Tanh-sinh quadrature, Serialized Form

Constructor Summary

Constructors

Constructor and Description
MixedRule(UnivariateRealFunction f, double a, double b, double c) Construct a MixedRule substitution rule.

Method Summary

Methods inherited from class com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.DoubleExponential

dx, ta, tb, x

Methods inherited from class java.lang.Object

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

Constructor Detail

MixedRule

public MixedRule(UnivariateRealFunction f,
                 double a,
                 double b,
                 double c)

Construct a MixedRule substitution rule.

Parameters:

f - the integrand

a - the lower limit

b - the upper limit

c - usually either 0 or 0.5 * PI