gy.c File Reference

Implements the integral of K_{5/3}(t) multiplied by y^n from y to infinity. More...

#include "mdb.h"
#include <math.h>

Go to the source code of this file.

Macros
#define	EPS   1.0e-8
#define	NY   5.0 / 3.0

Functions
double	gy (long n, double y)
	Compute the integral of K_{5/3}(t) scaled by y^n from y to infinity.

Detailed Description

Implements the integral of K_{5/3}(t) multiplied by y^n from y to infinity.

This file provides the implementation of gy(), which computes: inf. GY = y^n ∫ K_{5/3}(t) dt y The integral evaluation is based on methods described by V. O. Kostroun and uses exponential and hyperbolic function evaluations. It is generally reliable up to several decimal places for a range of inputs.

Copyright

• (c) 2002 The University of Chicago, as Operator of Argonne National Laboratory.
• (c) 2002 The Regents of the University of California, as Operator of Los Alamos National Laboratory.

License

This file is distributed under the terms of the Software License Agreement found in the file LICENSE included with this distribution.

Author

R. Dejus, H. Shang, R. Soliday, M. Borland

Definition in file gy.c.

Macro Definition Documentation

EPS

#define EPS   1.0e-8

Definition at line 27 of file gy.c.

NY

#define NY   5.0 / 3.0

Definition at line 28 of file gy.c.

Function Documentation

gy()

double gy	(	long	n,
		double	y )

Compute the integral of K_{5/3}(t) scaled by y^n from y to infinity.

This function calculates the integral: GY = y^n ∫ from t=y to t=∞ of K_{5/3}(t) dt. It uses a summation approach with an iterative increment (dt) and stops when subsequent terms are sufficiently small compared to the current sum.

Parameters

n	The exponent applied to y.
y	The lower limit of the integral.

Returns

The computed integral value GY.

Definition at line 42 of file gy.c.

                            {
  double p, sum, term, dt, gy;
 
  p = 1.0;
  sum = 0.0;
  dt = 0.1;
  term = exp(-y * cosh(p * dt)) * cosh(NY * p * dt) / cosh(p * dt);
  while (term > EPS * sum) {
    sum += term;
    p = p + 1;
    term = exp(-y * cosh(p * dt)) * cosh(NY * p * dt) / cosh(p * dt);
  }
  gy = pow(y, n) * dt * (sum + 0.5 * exp(-y));
  return gy;
}