using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Windows.Forms;
namespace SteadyStateTempCylinder
{
public partial class MainForm : Form
{
private double steps;
private int N, nsteps;
private BackgroundWorker bw;
private DateTime dt0;
private List<PotPoint> pts;
private double f(double r)
{
return r;
}
private double g(double r)
{
return r * r;
}
public MainForm()
{
InitializeComponent();
comboBox1.SelectedIndex = 0;
comboBox2.SelectedIndex = 0;
comboBox3.SelectedIndex = 0;
}
private void button1_Click(object sender, EventArgs e)
{
if (button1.Text.CompareTo("&Draw") == 0)
{
N = int.Parse((string)comboBox1.SelectedItem);
nsteps = int.Parse((string)comboBox2.SelectedItem);
steps = double.Parse((string)comboBox3.SelectedItem);
bw = new BackgroundWorker();
bw.DoWork += new DoWorkEventHandler(bw_DoWork);
bw.ProgressChanged += new ProgressChangedEventHandler(bw_ProgressChanged);
bw.RunWorkerCompleted += new RunWorkerCompletedEventHandler(bw_RunWorkerCompleted);
bw.WorkerReportsProgress = true;
bw.WorkerSupportsCancellation = true;
bw.RunWorkerAsync();
while (!bw.IsBusy) { }
button1.Text = "&Stop";
textBox1.Text = string.Empty;
}
else
bw.CancelAsync();
}
private void bw_ProgressChanged(object sender, ProgressChangedEventArgs e)
{
if (e.ProgressPercentage >= 0 && e.ProgressPercentage <= 100)
progressBar1.Value = e.ProgressPercentage;
}
private void bw_RunWorkerCompleted(object sender, RunWorkerCompletedEventArgs e)
{
try
{
DateTime dt1 = DateTime.Now;
TimeSpan ts = dt1 - dt0;
DrawGraphForm dgf = new DrawGraphForm(1.0, 1.0, pts);
dgf.Show();
button1.Text = "&Draw";
progressBar1.Value = 0;
textBox1.Text = ts.Hours.ToString("D2") + ":";
textBox1.Text += ts.Minutes.ToString("D2") + ":";
textBox1.Text += ts.Seconds.ToString("D2") + ".";
textBox1.Text += ts.Milliseconds.ToString("D3");
}
catch (Exception ex)
{
MessageBox.Show(ex.ToString(), "Warning Message",
MessageBoxButtons.OK, MessageBoxIcon.Warning);
}
}
private void bw_DoWork(object sender, DoWorkEventArgs e)
{
dt0 = DateTime.Now;
double step = 1.0 / Math.Sqrt(steps);
double percent = steps / 100.0;
int total = 0;
int count = 0;
pts = new List<PotPoint>();
double r = 0.0, z = 0.0;
double umin = double.MaxValue;
double umax = double.MinValue;
SteadyStateTemp sst = new SteadyStateTemp(1.0, 1.0, N, nsteps, f, g);
while (r <= 1.0)
{
z = 0.0;
while (z <= 1.0)
{
double u = sst.u(r, z);
PotPoint pt = new PotPoint(r, z, u);
pts.Add(pt);
z += step;
count++;
if (count >= percent)
{
count = 0;
total++;
bw.ReportProgress(total);
}
if (u < umin)
umin = u;
if (u > umax)
umax = u;
}
r += step;
}
}
}
}using System;
namespace SteadyStateTempCylinder
{
class SteadyStateTemp
{
private double A, B;
private double[] Jn;
private double[] lambda;
private int N, n, nsteps;
private BesselFunctions bf;
private Func<double, double> f;
Func<double, double> g;
public SteadyStateTemp(
double A,
double B,
int N, int nsteps,
Func<double, double> f,
Func<double, double> g)
{
double[] zeros = new double[N];
this.A = A;
this.B = B;
this.N = N;
this.nsteps = nsteps;
this.f = f;
this.g = g;
Jn = new double[N + 1];
lambda = new double[N + 1];
bf = new BesselFunctions();
bf.besszeros(1, N, zeros, 1);
for (n = 1; n <= N; n++)
{
lambda[n] = zeros[n - 1];
Jn[n] = J();
}
}
private double SimpsonsRule(double lower, double upper, Func<double, double> f)
{
double h = (upper - lower) / nsteps;
double h2 = 2.0 * h;
double s = 0.0;
double t = 0.0;
double x = lower + h;
for (int i = 1; i < nsteps; i += 2)
{
s += f(x);
x += h2;
}
x = lower + h2;
for (int i = 2; i < nsteps; i += 2)
{
t += f(x);
x += h2;
}
return h * (f(lower) + 4 * s + 2 * t + f(upper)) / 3.0;
}
private double IIntegrand(double r)
{
return bf.bessj0(lambda[n] * r) * r;
}
private double I()
{
return SimpsonsRule(0.0, A, IIntegrand);
}
private double JIntegrand(double r)
{
double b0 = bf.bessj0(lambda[n] * r);
return b0 * b0 * r;
}
private double J()
{
return SimpsonsRule(0.0, A, JIntegrand);
}
private double KIntegrand(double r)
{
return bf.bessj0(lambda[n] * r) * f(r) * r;
}
private double K()
{
return SimpsonsRule(0.0, A, KIntegrand);
}
private double LIntegrand(double r)
{
return bf.bessj0(lambda[n] * r) * g(r) * r;
}
private double L()
{
return SimpsonsRule(0.0, A, LIntegrand);
}
public double u(double r, double z)
{
double sum = 0.0;
for (n = 1; n <= N; n++)
{
double denom = Math.Sinh(lambda[n] * B);
double J0 = bf.bessj0(lambda[n] * r);
double an = L() / Jn[n];
double bn = K() / Jn[n];
sum += J0 * an * Math.Sinh(lambda[n] * z) / denom;
sum += J0 * bn * Math.Sinh(lambda[n] * (B - z)) / denom;
}
return sum;
}
}
}using System;
namespace SteadyStateTempCylinder
{
class BesselFunctions
{
public double bessj0(double x)
{
if (x == 0.0) return 1.0;
if (Math.Abs(x) < 8.0)
{
int i;
double z, z2, b0, b1, b2;
double[] ar ={-0.75885e-15, 0.4125321e-13,
-0.194383469e-11, 0.7848696314e-10, -0.267925353056e-8,
0.7608163592419e-7, -0.176194690776215e-5,
0.324603288210051e-4, -0.46062616620628e-3,
0.48191800694676e-2, -0.34893769411409e-1,
0.158067102332097, -0.37009499387265, 0.265178613203337,
-0.872344235285222e-2};
x /= 8.0;
z = 2.0 * x * x - 1.0;
z2 = z + z;
b1 = b2 = 0.0;
for (i = 0; i <= 14; i++)
{
b0 = z2 * b1 - b2 + ar[i];
b2 = b1;
b1 = b0;
}
return z * b1 - b2 + 0.15772797147489;
}
else
{
double c, cosx, sinx, p0 = 0.0, q0 = 0.0;
x = Math.Abs(x);
c = 0.797884560802865 / Math.Sqrt(x);
cosx = Math.Cos(x - 0.706858347057703e1);
sinx = Math.Sin(x - 0.706858347057703e1);
besspq0(x, ref p0, ref q0);
return c * (p0 * cosx - q0 * sinx);
}
}
public double bessj1(double x)
{
if (x == 0.0) return 1.0;
if (Math.Abs(x) < 8.0)
{
int i;
double z, z2, b0, b1, b2;
double[] ar ={-0.19554e-15, 0.1138572e-13,
-0.57774042e-12, 0.2528123664e-10, -0.94242129816e-9,
0.2949707007278e-7, -0.76175878054003e-6,
0.158870192399321e-4, -0.260444389348581e-3,
0.324027018268386e-2, -0.291755248061542e-1,
0.177709117239728e0, -0.661443934134543e0,
0.128799409885768e1, -0.119180116054122e1};
x /= 8.0;
z = 2.0 * x * x - 1.0;
z2 = z + z;
b1 = b2 = 0.0;
for (i = 0; i <= 14; i++)
{
b0 = z2 * b1 - b2 + ar[i];
b2 = b1;
b1 = b0;
}
return x * (z * b1 - b2 + 0.648358770605265);
}
else
{
int sgnx;
double c, cosx, sinx, p1 = 0.0, q1 = 0.0;
sgnx = (x > 0.0) ? 1 : -1;
x = Math.Abs(x);
c = 0.797884560802865 / Math.Sqrt(x);
cosx = Math.Cos(x - 0.706858347057703e1);
sinx = Math.Sin(x - 0.706858347057703e1);
besspq1(x, ref p1, ref q1);
return sgnx * c * (p1 * sinx + q1 * cosx);
}
}
private void besspq0(double x, ref double p0, ref double q0)
{
if (x < 8.0)
{
double b, cosx, sinx, j0x = 0.0, y0 = 0.0;
b = Math.Sqrt(x) * 1.25331413731550;
bessy01(x, ref y0, ref j0x);
j0x = bessj0(x);
x -= 0.785398163397448;
cosx = Math.Cos(x);
sinx = Math.Sin(x);
p0 = b * (y0 * sinx + j0x * cosx);
q0 = b * (y0 * cosx - j0x * sinx);
}
else
{
int i;
double x2, b0, b1, b2, y;
double[] ar1 ={-0.10012e-15, 0.67481e-15, -0.506903e-14,
0.4326596e-13, -0.43045789e-12, 0.516826239e-11,
-0.7864091377e-10, 0.163064646352e-8, -0.5170594537606e-7,
0.30751847875195e-5, -0.536522046813212e-3};
double[] ar2 ={-0.60999e-15, 0.425523e-14,
-0.3336328e-13, 0.30061451e-12, -0.320674742e-11,
0.4220121905e-10, -0.72719159369e-9, 0.1797245724797e-7,
-0.74144984110606e-6, 0.683851994261165e-4};
y = 8.0 / x;
x = 2.0 * y * y - 1.0;
x2 = x + x;
b1 = b2 = 0.0;
for (i = 0; i <= 10; i++)
{
b0 = x2 * b1 - b2 + ar1[i];
b2 = b1;
b1 = b0;
}
p0 = x * b1 - b2 + 0.99946034934752;
b1 = b2 = 0.0;
for (i = 0; i <= 9; i++)
{
b0 = x2 * b1 - b2 + ar2[i];
b2 = b1;
b1 = b0;
}
q0 = (x * b1 - b2 - 0.015555854605337) * y;
}
}
private void besspq1(double x, ref double p1, ref double q1)
{
if (x < 8.0)
{
double b, cosx, sinx, j1x = 0.0, y1 = 0.0;
b = Math.Sqrt(x) * 1.25331413731550;
bessy01(x, ref j1x, ref y1);
j1x = bessj1(x);
x -= 0.785398163397448;
cosx = Math.Cos(x);
sinx = Math.Sin(x);
p1 = b * (j1x * sinx - y1 * cosx);
q1 = b * (j1x * cosx + y1 * sinx);
}
else
{
int i;
double x2, b0, b1, b2, y;
double[] ar1 ={0.10668e-15, -0.72212e-15, 0.545267e-14,
-0.4684224e-13, 0.46991955e-12, -0.570486364e-11,
0.881689866e-10, -0.187189074911e-8, 0.6177633960644e-7,
-0.39872843004889e-5, 0.89898983308594e-3};
double[] ar2 ={-0.10269e-15, 0.65083e-15, -0.456125e-14,
0.3596777e-13, -0.32643157e-12, 0.351521879e-11,
-0.4686363688e-10, 0.82291933277e-9, -0.2095978138408e-7,
0.91386152579555e-6, -0.96277235491571e-4};
y = 8.0 / x;
x = 2.0 * y * y - 1.0;
x2 = x + x;
b1 = b2 = 0.0;
for (i = 0; i <= 10; i++)
{
b0 = x2 * b1 - b2 + ar1[i];
b2 = b1;
b1 = b0;
}
p1 = x * b1 - b2 + 1.0009030408600137;
b1 = b2 = 0.0;
for (i = 0; i <= 10; i++)
{
b0 = x2 * b1 - b2 + ar2[i];
b2 = b1;
b1 = b0;
}
q1 = (x * b1 - b2 + 0.46777787069535e-1) * y;
}
}
private void bessy01(double x, ref double y0, ref double y1)
{
if (x < 8.0)
{
int i;
double z, z2, c, lnx, b0, b1, b2;
double[] ar1 ={0.164349e-14, -0.8747341e-13,
0.402633082e-11, -0.15837552542e-9, 0.524879478733e-8,
-0.14407233274019e-6, 0.32065325376548e-5,
-0.563207914105699e-4, 0.753113593257774e-3,
-0.72879624795521e-2, 0.471966895957634e-1,
-0.177302012781143, 0.261567346255047,
0.179034314077182, -0.274474305529745};
double[] ar2 ={0.42773e-15, -0.2440949e-13,
0.121143321e-11, -0.5172121473e-10, 0.187547032473e-8,
-0.5688440039919e-7, 0.141662436449235e-5,
-0.283046401495148e-4, 0.440478629867099e-3,
-0.51316411610611e-2, 0.423191803533369e-1,
-0.226624991556755, 0.675615780772188,
-0.767296362886646, -0.128697384381350};
c = 0.636619772367581;
lnx = c * Math.Log(x);
c /= x;
x /= 8.0;
z = 2.0 * x * x - 1.0;
z2 = z + z;
b1 = b2 = 0.0;
for (i = 0; i <= 14; i++)
{
b0 = z2 * b1 - b2 + ar1[i];
b2 = b1;
b1 = b0;
}
y0 = lnx * bessj0(8.0 * x) + z * b1 - b2 - 0.33146113203285e-1;
b1 = b2 = 0.0;
for (i = 0; i <= 14; i++)
{
b0 = z2 * b1 - b2 + ar2[i];
b2 = b1;
b1 = b0;
}
y1 = lnx * bessj1(8.0 * x) - c + x * (z * b1 - b2 + 0.2030410588593425e-1);
}
else
{
double c, cosx, sinx, p0 = 0.0, q0 = 0.0, p1 = 0.0, q1 = 0.0;
c = 0.797884560802865 / Math.Sqrt(x);
besspq0(x, ref p0, ref q0);
besspq1(x, ref p1, ref q1);
x -= 0.706858347057703e1;
cosx = Math.Cos(x);
sinx = Math.Sin(x);
y0 = c * (p0 * sinx + q0 * cosx);
y1 = c * (q1 * sinx - p1 * cosx);
}
}
private double recipgamma(double x, ref double odd, ref double even)
{
int i;
double alfa, beta, x2;
double[] b = new double[13];
b[1] = -0.283876542276024; b[2] = -0.076852840844786;
b[3] = 0.001706305071096; b[4] = 0.001271927136655;
b[5] = 0.000076309597586; b[6] = -0.000004971736704;
b[7] = -0.000000865920800; b[8] = -0.000000033126120;
b[9] = 0.000000001745136; b[10] = 0.000000000242310;
b[11] = 0.000000000009161; b[12] = -0.000000000000170;
x2 = x * x * 8.0;
alfa = -0.000000000000001;
beta = 0.0;
for (i = 12; i >= 2; i -= 2)
{
beta = -(alfa * 2.0 + beta);
alfa = -beta * x2 - alfa + b[i];
}
even = (beta / 2.0 + alfa) * x2 - alfa + 0.921870293650453;
alfa = -0.000000000000034;
beta = 0.0;
for (i = 11; i >= 1; i -= 2)
{
beta = -(alfa * 2.0 + beta);
alfa = -beta * x2 - alfa + b[i];
}
odd = (alfa + beta) * 2.0;
return odd * x + even;
}
private void bessya01(double a, double x, ref double ya, ref double ya1)
{
if (a == 0.0)
{
bessy01(x, ref ya, ref ya1);
}
else
{
bool rec, rev;
int n, na;
double b, c, d, e, f, g, h = 0.0, p = 0.0, pi, q = 0.0, r, s;
pi = Math.PI;
na = (int)Math.Floor(a + 0.5);
rec = (a >= 0.5);
rev = (a < -0.5);
if (rev || rec) a -= na;
if (a == -0.5)
{
p = Math.Sqrt(2.0 / pi / x);
f = p * Math.Sin(x);
g = -p * Math.Cos(x);
}
else if (x < 3.0)
{
b = x / 2.0;
d = -Math.Log(b);
e = a * d;
c = (Math.Abs(a) < 1.0e-8) ? 1.0 / pi : a / Math.Sin(a * pi);
s = (Math.Abs(e) < 1.0e-8) ? 1.0 : Math.Sinh(e) / e;
e = Math.Exp(e);
g = recipgamma(a, ref p, ref q) * e;
e = (e + 1.0 / e) / 2.0;
f = 2.0 * c * (p * e + q * s * d);
e = a * a;
p = g * c;
q = 1.0 / g / pi;
c = a * pi / 2.0;
r = (Math.Abs(c) < 1.0e-8) ? 1.0 : Math.Sin(c) / c;
r *= pi * c * r;
c = 1.0;
d = -b * b;
ya = f + r * q;
ya1 = p;
n = 1;
do
{
f = (f * n + p + q) / (n * n - e);
c = c * d / n;
p /= (n - a);
q /= (n + a);
g = c * (f + r * q);
h = c * p - n * g;
ya += g;
ya1 += h;
n++;
} while (Math.Abs(g / (1.0 + Math.Abs(ya))) + Math.Abs(h / (1.0 + Math.Abs(ya1))) >
1.0e-15);
f = -ya;
g = -ya1 / b;
}
else
{
b = x - pi * (a + 0.5) / 2.0;
c = Math.Cos(b);
s = Math.Sin(b);
d = Math.Sqrt(2.0 / x / pi);
besspqa01(a, x, ref p, ref q, ref b, ref h);
f = d * (p * s + q * c);
g = d * (h * s - b * c);
}
if (rev)
{
x = 2.0 / x;
na = -na - 1;
for (n = 0; n <= na; n++)
{
h = x * (a - n) * f - g;
g = f;
f = h;
}
}
else if (rec)
{
x = 2.0 / x;
for (n = 1; n <= na; n++)
{
h = x * (a + n) * g - f;
f = g;
g = h;
}
}
ya = f;
ya1 = g;
}
}
private int start(double x, int n, int t)
{
int s;
double p, q, r, y;
s = 2 * t - 1;
p = 36.0 / x - t;
r = n / x;
if (r > 1.0 || t == 1)
{
q = Math.Sqrt(r * r + s);
r = r * Math.Log(q + r) - q;
}
else
r = 0.0;
q = 18.0 / x + r;
r = (p > q) ? p : q;
p = Math.Sqrt(2.0 * (t + r));
p = x * ((1.0 + r) + p) / (1.0 + p);
y = 0.0;
q = y;
do
{
y = p;
p /= x;
q = Math.Sqrt(p * p + s);
p = x * (r + q) / Math.Log(p + q);
q = y;
} while (p > q || p < q - 1.0);
return (t == 1) ? (int)Math.Floor(p + 1.0) : -(int)Math.Floor(-p / 2.0) * 2;
}
public void bessj(double x, int n, double[] j)
{
if (x == 0.0)
{
j[0] = 1.0;
for (; n >= 1; n--) j[n] = 0.0;
}
else
{
int l, m, nu, signx;
double x2, r, s;
signx = (x > 0.0) ? 1 : -1;
x = Math.Abs(x);
r = s = 0.0;
x2 = 2.0 / x;
l = 0;
nu = start(x, n, 0);
for (m = nu; m >= 1; m--)
{
r = 1.0 / (x2 * m - r);
l = 2 - l;
s = r * (l + s);
if (m <= n) j[m] = r;
}
j[0] = r = 1.0 / (1.0 + s);
for (m = 1; m <= n; m++) r = j[m] *= r;
if (signx < 0.0)
for (m = 1; m <= n; m += 2) j[m] = -j[m];
}
}
private void spherbessj(double x, int n, double[] j)
{
if (x == 0.0)
{
j[0] = 1.0;
for (; n >= 1; n--) j[n] = 0.0;
}
else if (n == 0)
{
double x2;
if (Math.Abs(x) < 0.015)
{
x2 = x * x / 6.0;
j[0] = 1.0 + x2 * (x2 * 0.3 - 1.0);
}
else
j[0] = Math.Sin(x) / x;
}
else
{
int m;
double r, s;
r = 0.0;
m = start(x, n, 0);
for (; m >= 1; m--)
{
r = 1.0 / ((m + m + 1) / x - r);
if (m <= n) j[m] = r;
}
if (x < 0.015)
{
s = x * x / 6.0;
j[0] = r = s * (s * 0.3 - 1.0) + 1.0;
}
else
j[0] = r = Math.Sin(x) / x;
for (m = 1; m <= n; m++) r = j[m] *= r;
}
}
private double loggamma(double x)
{
int i;
double r, x2, y, f, u0, u1, u, z;
double[] b = new double[19];
if (x > 13.0)
{
r = 1.0;
while (x <= 22.0)
{
r /= x;
x += 1.0;
}
x2 = -1.0 / (x * x);
r = Math.Log(r);
return Math.Log(x) * (x - 0.5) - x + r + 0.918938533204672 +
(((0.595238095238095e-3 * x2 + 0.793650793650794e-3) * x2 +
0.277777777777778e-2) * x2 + 0.833333333333333e-1) / x;
}
else
{
f = 1.0;
u0 = u1 = 0.0;
b[1] = -0.0761141616704358; b[2] = 0.0084323249659328;
b[3] = -0.0010794937263286; b[4] = 0.0001490074800369;
b[5] = -0.0000215123998886; b[6] = 0.0000031979329861;
b[7] = -0.0000004851693012; b[8] = 0.0000000747148782;
b[9] = -0.0000000116382967; b[10] = 0.0000000018294004;
b[11] = -0.0000000002896918; b[12] = 0.0000000000461570;
b[13] = -0.0000000000073928; b[14] = 0.0000000000011894;
b[15] = -0.0000000000001921; b[16] = 0.0000000000000311;
b[17] = -0.0000000000000051; b[18] = 0.0000000000000008;
if (x < 1.0)
{
f = 1.0 / x;
x += 1.0;
}
else
while (x > 2.0)
{
x -= 1.0;
f *= x;
}
f = Math.Log(f);
y = x + x - 3.0;
z = y + y;
for (i = 18; i >= 1; i--)
{
u = u0;
u0 = z * u0 + b[i] - u1;
u1 = u;
}
return (u0 * y + 0.491415393029387 - u1) * (x - 1.0) * (x - 2.0) + f;
}
}
private double gamma(double x)
{
int inv;
double y, s, f = 0.0, g, odd = 0.0, even = 0.0;
if (x < 0.5)
{
y = x - Math.Floor(x / 2.0) * 2;
s = Math.PI;
if (y >= 1.0)
{
s = -s;
y = 2.0 - y;
}
if (y >= 0.5) y = 1.0 - y;
inv = 1;
x = 1.0 - x;
f = s / Math.Sin(3.14159265358979 * y);
}
else
inv = 0;
if (x > 22.0)
g = Math.Exp(loggamma(x));
else
{
s = 1.0;
while (x > 1.5)
{
x = x - 1.0;
s *= x;
}
g = s / recipgamma(1.0 - x, ref odd, ref even);
}
return (inv == 1 ? f / g : g);
}
private void bessjaplusn(double a, double x, int n, double[] ja)
{
if (x == 0.0)
{
ja[0] = (a == 0.0) ? 1.0 : 0.0;
for (; n >= 1; n--) ja[n] = 0.0;
}
else if (a == 0.0)
{
bessj(x, n, ja);
}
else if (a == 0.5)
{
double s;
s = Math.Sqrt(x) * 0.797884560802865;
spherbessj(x, n, ja);
for (; n >= 0; n--) ja[n] *= s;
}
else
{
int k, m, nu;
double a2, x2, r, s, l, labda;
l = 1.0;
nu = start(x, n, 0);
for (m = 1; m <= nu; m++) l = l * (m + a) / (m + 1);
r = s = 0.0;
x2 = 2.0 / x;
k = -1;
a2 = a + a;
for (m = nu + nu; m >= 1; m--)
{
r = 1.0 / (x2 * (a + m) - r);
if (k == 1)
labda = 0.0;
else
{
l = l * (m + 2) / (m + a2);
labda = l * (m + a);
}
s = r * (labda + s);
k = -k;
if (m <= n) ja[m] = r;
}
ja[0] = r = 1.0 / gamma(1.0 + a) / (1.0 + s) / Math.Pow(x2, a);
for (m = 1; m <= n; m++) r = ja[m] *= r;
}
}
private void besspqa01(double a, double x, ref double pa, ref double qa,
ref double pa1, ref double qa1)
{
if (a == 0.0)
{
besspq0(x, ref pa, ref qa);
besspq1(x, ref pa1, ref qa1);
}
else
{
bool rec, rev;
int n, na = 0;
double b, pi, p0, q0;
pi = Math.PI;
rev = a < -0.5;
if (rev) a = -a - 1.0;
rec = a >= 0.5;
if (rec)
{
na = (int)Math.Floor(a + 0.5);
a -= na;
}
if (a == -0.5)
{
pa = pa1 = 1.0;
qa = qa1 = 0.0;
}
else if (x >= 3.0)
{
double c, d, e, f, g, p, q, r, s, temp;
c = 0.25 - a * a;
b = x + x;
f = r = 1.0;
g = -x;
s = 0.0;
temp = x * Math.Cos(a * pi) / pi * 1.0e15;
e = temp * temp;
n = 2;
do
{
d = (n - 1 + c / n);
p = (2 * n * f + b * g - d * r) / (n + 1);
q = (2 * n * g - b * f - d * s) / (n + 1);
r = f;
f = p;
s = g;
g = q;
n++;
} while ((p * p + q * q) * n * n < e);
e = f * f + g * g;
p = (r * f + s * g) / e;
q = (s * f - r * g) / e;
f = p;
g = q;
n--;
while (n > 0)
{
r = (n + 1) * (2.0 - p) - 2.0;
s = b + (n + 1) * q;
d = (n - 1 + c / n) / (r * r + s * s);
p = d * r;
q = d * s;
e = f;
f = p * (e + 1.0) - g * q;
g = q * (e + 1.0) + p * g;
n--;
}
f += 1.0;
d = f * f + g * g;
pa = f / d;
qa = -g / d;
d = a + 0.5 - p;
q += x;
pa1 = (pa * q - qa * d) / x;
qa1 = (qa * q + pa * d) / x;
}
else
{
double c, s, chi, ya = 0.0, ya1 = 0.0;
double[] ja = new double[2];
b = Math.Sqrt(pi * x / 2.0);
chi = x - pi * (a / 2.0 + 0.25);
c = Math.Cos(chi);
s = Math.Sin(chi);
bessya01(a, x, ref ya, ref ya1);
bessjaplusn(a, x, 1, ja);
pa = b * (ya * s + c * ja[0]);
qa = b * (c * ya - s * ja[0]);
pa1 = b * (s * ja[1] - c * ya1);
qa1 = b * (c * ja[1] + s * ya1);
}
if (rec)
{
x = 2.0 / x;
b = (a + 1.0) * x;
for (n = 1; n <= na; n++)
{
p0 = pa - qa1 * b;
q0 = qa + pa1 * b;
pa = pa1;
pa1 = p0;
qa = qa1;
qa1 = q0;
b += x;
}
}
if (rev)
{
p0 = pa1;
pa1 = pa;
pa = p0;
q0 = qa1;
qa1 = qa;
qa = q0;
}
}
}
public void besszeros(double a, int n, double[] z, int d)
{
int j, s;
double aa, a2, b, bb, c, chi, co, mu, mu2, mu3, mu4, p, pi, pa = 0.0, pa1 = 0.0, p0, p1, pp1,
q, qa = 0.0, qa1 = 0.0, q1, qq1, ro, si, t, tt, u, v, w, x, xx, x4, y, yy, fi;
pi = Math.PI;
aa = a * a;
mu = 4.0 * aa;
mu2 = mu * mu;
mu3 = mu * mu2;
mu4 = mu2 * mu2;
if (d < 3)
{
p = 7.0 * mu - 31.0;
p0 = mu - 1.0;
p1 = 4.0 * (253.0 * mu2 - 3722.0 * mu + 17869.0) / 15.0 / p * p0;
q1 = 8.0 * (83.0 * mu2 - 982.0 * mu + 3779.0) / 5.0 / p;
}
else
{
p = 7.0 * mu2 + 82.0 * mu - 9.0;
p0 = mu + 3.0;
p1 = (4048.0 * mu4 + 131264.0 * mu3 - 221984.0 * mu2 -
417600.0 * mu + 1012176.0) / 60.0 / p;
q1 = 1.6 * (83.0 * mu3 + 2075.0 * mu2 - 3039.0 * mu + 3537.0) / p;
}
t = (d == 1 || d == 4) ? 0.25 : 0.75;
tt = 4.0 * t;
if (d < 3)
{
pp1 = 5.0 / 48.0;
qq1 = -5.0 / 36.0;
}
else
{
pp1 = -7.0 / 48.0;
qq1 = 35.0 / 288.0;
}
y = 3.0 * pi / 8.0;
bb = (a >= 3.0) ? Math.Pow(a, -2.0 / 3.0) : 0.0;
for (s = 1; s <= n; s++)
{
if (a == 0.0 && s == 1 && d == 3)
{
x = 0.0;
j = 0;
}
else
{
if (s >= 3.0 * a - 8.0)
{
b = (s + a / 2.0 - t) * pi;
c = 1.0 / b / b / 64.0;
x = b - 1.0 / b / 8.0 * (p0 - p1 * c) / (1.0 - q1 * c);
}
else
{
if (s == 1)
x = ((d == 1) ? -2.33811 : ((d == 2) ? -1.17371 :
((d == 3) ? -1.01879 : -2.29444)));
else
{
x = y * (4.0 * s - tt);
v = 1.0 / x / x;
x = -Math.Pow(x, 2.0 / 3.0) * (1.0 + v * (pp1 + qq1 * v));
}
u = x * bb;
yy = 2.0 / 3.0 * Math.Pow(-u, 1.5);
if (yy == 0.0)
fi = 0.0;
else if (yy > 1.0e5)
fi = 1.570796;
else
{
double r, pp;
if (yy < 1.0)
{
p = Math.Pow(3.0 * yy, 1.0 / 3.0);
pp = p * p;
p *= (1.0 + pp * (-210.0 + pp * (27.0 - 2.0 * pp)) / 1575.0);
}
else
{
p = 1.0 / (yy + 1.570796);
pp = p * p;
p = 1.570796 - p * (1.0 + pp * (2310.0 + pp * (3003.0 + pp *
(4818.0 + pp * (8591.0 + pp * 16328.0)))) / 3465.0);
}
pp = (yy + p) * (yy + p);
r = (p - Math.Atan(p + yy)) / pp;
fi = p - (1.0 + pp) * r * (1.0 + r / (p + yy));
}
v = fi;
w = 1.0 / Math.Cos(v);
xx = 1.0 - w * w;
c = Math.Sqrt(u / xx);
x = w * (a + c / a / u * ((d < 3) ?
-5.0 / 48.0 / u - c * (-5.0 / 24.0 / xx + 1.0 / 8.0) :
7.0 / 48.0 / u + c * (-7.0 / 24.0 / xx + 3.0 / 8.0)));
}
j = 0;
do
{
xx = x * x;
x4 = xx * xx;
a2 = aa - xx;
besspqa01(a, x, ref pa, ref qa, ref pa1, ref qa1);
chi = x - pi * (a / 2.0 + 0.25);
si = Math.Sin(chi);
co = Math.Cos(chi);
ro = ((d == 1) ? (pa * co - qa * si) / (pa1 * si + qa1 * co) :
((d == 2) ? (pa * si + qa * co) / (qa1 * si - pa1 * co) :
((d == 3) ? a / x - (pa1 * si + qa1 * co) / (pa * co - qa * si) :
a / x - (qa1 * si - pa1 * co) / (pa * si + qa * co))));
j++;
if (d < 3)
{
u = ro;
p = (1.0 - 4.0 * a2) / 6.0 / x / (2.0 * a + 1.0);
q = (2.0 * (xx - mu) - 1.0 - 6.0 * a) / 3.0 / x / (2.0 * a + 1.0);
}
else
{
u = -xx * ro / a2;
v = 2.0 * x * a2 / (aa + xx) / 3.0;
w = a2 * a2 * a2;
q = v * (1.0 + (mu2 + 32.0 * mu * xx + 48.0 * x4) / 32.0 / w);
p = v * (1.0 + (-mu2 + 40.0 * mu * xx + 48.0 * x4) / 64.0 / w);
}
w = u * (1.0 + p * ro) / (1.0 + q * ro);
x += w;
} while (Math.Abs(w / x) > 1.0e-13 && j < 5);
}
z[s - 1] = x;
}
}
}
}using System;
using System.Collections.Generic;
using System.Drawing;
using System.Windows.Forms;
namespace SteadyStateTempCylinder
{
public partial class DrawGraphForm : Form
{
private const double epsilon = 1.0e-2;
private double xMax;
private double yMax;
private int n;
private Brush brush;
private Brush potBrush;
private Font font;
private Pen pen1, pen2;
private List<PotPoint> pts;
public DrawGraphForm(
double xMax,
double yMax,
List<PotPoint> pts)
{
InitializeComponent();
this.xMax = xMax;
this.yMax = yMax;
this.pts = pts;
n = pts.Count;
brush = new SolidBrush(Color.Black);
potBrush = new SolidBrush(Color.Red);
pen1 = new Pen(Color.Black);
pen2 = new Pen(Color.Blue);
font = new Font("Courier New", 12f, FontStyle.Bold);
panel1.Paint += new PaintEventHandler(PanelPaintHandler);
}
private void DrawGraph(float u0, float v0,
float u1, float v1,
Graphics g)
{
try
{
float xMin = u0;
float yMin = v0;
float xMax = u1;
float yMax = v1;
float xSpan = xMax - xMin;
float ySpan = yMax - yMin;
float deltaX = xSpan / 8.0f;
float deltaY = ySpan / 8.0f;
float height = panel1.Height;
float width = panel1.Width;
float sx0 = 2f * width / 16f;
float sx1 = 14f * width / 16f;
float sy0 = 2f * height / 16f;
float sy1 = 14f * height / 16f;
float xSlope = (sx1 - sx0) / xSpan;
float xInter = sx0 - xSlope * xMin;
float ySlope = (sy0 - sy1) / ySpan;
float yInter = sy0 - ySlope * yMax;
float x = xMin;
float y = yMin;
string fTitle = "Graph of Constant u";
float w = g.MeasureString(fTitle, font).Width;
float h = g.MeasureString(fTitle, font).Height;
g.DrawString(fTitle, font, brush,
(width - w) / 2f, h);
string xTitle = "r";
w = g.MeasureString(xTitle, font).Width;
g.DrawString(xTitle, font, brush,
sx0 + (sx1 - sx0 - w) / 2f, sy1 + h + h);
string yTitle = "z";
w = g.MeasureString(yTitle, font).Width;
g.DrawString(yTitle, font, brush,
sx1 + w / 5f, sy0 + (sy1 - sy0) / 2f - h / 2f);
int i = 0;
while (i <= 8)
{
float sx = xSlope * x + xInter;
string s = string.Format("{0,5:0.00}", x);
g.DrawLine(pen1, sx, sy0, sx, sy1);
w = g.MeasureString(s, font).Width;
g.DrawString(s, font, brush,
sx - w / 2, sy1 + h / 2f);
x += deltaX;
i++;
}
i = 0;
while (i <= 8)
{
float sy = ySlope * y + yInter;
string s = string.Format("{0,5:0.00}", y);
w = g.MeasureString(s, font).Width;
g.DrawLine(pen1, sx0, sy, sx1, sy);
g.DrawString(s, font, brush,
sx0 - w - w / 5f, sy - h / 2f);
y += deltaY;
i++;
}
g.Clip = new Region(new RectangleF(
sx0, sy0, (sx1 - sx0), (sy1 - sy0)));
for (i = 0; i < n; i++)
{
float px = (float)pts[i].X;
float py = (float)pts[i].Y;
float pu = (float)pts[i].U;
if (Math.Abs(pu + 0.05) < epsilon ||
Math.Abs(pu + 0.10) < epsilon ||
Math.Abs(pu + 0.15) < epsilon ||
Math.Abs(pu + 0.20) < epsilon ||
Math.Abs(pu + 0.25) < epsilon ||
Math.Abs(pu + 0.30) < epsilon ||
Math.Abs(pu + 0.35) < epsilon ||
Math.Abs(pu + 0.40) < epsilon ||
Math.Abs(pu + 0.45) < epsilon ||
Math.Abs(pu + 0.50) < epsilon ||
Math.Abs(pu + 0.55) < epsilon ||
Math.Abs(pu + 0.60) < epsilon ||
Math.Abs(pu + 0.55) < epsilon ||
Math.Abs(pu + 0.70) < epsilon ||
Math.Abs(pu + 0.75) < epsilon ||
Math.Abs(pu + 0.80) < epsilon ||
Math.Abs(pu + 0.85) < epsilon ||
Math.Abs(pu + 0.90) < epsilon ||
Math.Abs(pu + 0.95) < epsilon ||
Math.Abs(pu - 0.05) < epsilon ||
Math.Abs(pu - 0.10) < epsilon ||
Math.Abs(pu - 0.15) < epsilon ||
Math.Abs(pu - 0.20) < epsilon ||
Math.Abs(pu - 0.25) < epsilon ||
Math.Abs(pu - 0.30) < epsilon ||
Math.Abs(pu - 0.35) < epsilon ||
Math.Abs(pu - 0.40) < epsilon ||
Math.Abs(pu - 0.45) < epsilon ||
Math.Abs(pu - 0.50) < epsilon ||
Math.Abs(pu - 0.55) < epsilon ||
Math.Abs(pu - 0.60) < epsilon ||
Math.Abs(pu - 0.55) < epsilon ||
Math.Abs(pu - 0.70) < epsilon ||
Math.Abs(pu - 0.75) < epsilon ||
Math.Abs(pu - 0.80) < epsilon ||
Math.Abs(pu - 0.85) < epsilon ||
Math.Abs(pu - 0.90) < epsilon ||
Math.Abs(pu - 0.95) < epsilon)
{
float sx = xSlope * px + xInter;
float sy = ySlope * py + yInter;
g.FillEllipse(potBrush, (float)sx, (float)sy, 2.0f, 2.0f);
}
}
}
catch (Exception ex)
{
MessageBox.Show(ex.ToString(), "Warning Message",
MessageBoxButtons.OK, MessageBoxIcon.Warning);
}
}
private void LayOutTheForm()
{
// layout the panel
int w = ClientSize.Width;
int h = ClientSize.Height;
panel1.Width = w;
panel1.Height = h;
panel1.Location = new Point(0, 0);
panel1.Invalidate();
}
protected void PanelPaintHandler(object sender, PaintEventArgs pa)
{
DrawGraph((float)0.0, (float)0.0, (float)xMax, (float)yMax, pa.Graphics);
}
protected override void OnResize(EventArgs ea)
{
LayOutTheForm();
}
}
}using System;
namespace SteadyStateTempCylinder
{
public class PotPoint : IComparable
{
private double x, y, u;
public double X
{
get
{
return x;
}
set
{
x = value;
}
}
public double Y
{
get
{
return y;
}
set
{
y = value;
}
}
public double U
{
get
{
return u;
}
set
{
u = value;
}
}
public PotPoint(double x, double y, double u)
{
this.x = x;
this.y = y;
this.u = u;
}
public int CompareTo(object obj)
{
if (obj == null)
return 1;
PotPoint pp = (PotPoint)obj;
if (u > pp.u)
return 1;
else if (u == pp.u)
return 0;
else
return -1;
}
}
}
Author: jamespatewilliamsjr
My whole legal name is James Pate Williams, Jr. I was born in LaGrange, Georgia approximately 70 years ago. I barely graduated from LaGrange High School with low marks in June 1971. Later in June 1979, I graduated from LaGrange College with a Bachelor of Arts in Chemistry with a little over a 3 out 4 Grade Point Average (GPA). In the Spring Quarter of 1978, I taught myself how to program a Texas Instruments desktop programmable calculator and in the Summer Quarter of 1978 I taught myself Dayton BASIC (Beginner's All-purpose Symbolic Instruction Code) on LaGrange College's Data General Eclipse minicomputer. I took courses in BASIC in the Fall Quarter of 1978 and FORTRAN IV (Formula Translator IV) in the Winter Quarter of 1979. Professor Kenneth Cooper, a genius poly-scientist taught me a course in the Intel 8085 microprocessor architecture and assembly and machine language. We would hand assemble our programs and insert the resulting machine code into our crude wooden box computer which was designed and built by Professor Cooper. From 1990 to 1994 I earned a Bachelor of Science in Computer Science from LaGrange College. I had a 4 out of 4 GPA in the period 1990 to 1994. I took courses in C, COBOL, and Pascal during my BS work. After graduating from LaGrange College a second time in May 1994, I taught myself C++. In December 1995, I started using the Internet and taught myself client-server programming. I created a website in 1997 which had C and C# implementations of algorithms from the "Handbook of Applied Cryptography" by Alfred J. Menezes, et. al., and some other cryptography and number theory textbooks and treatises.
View all posts by jamespatewilliamsjr
Numerical Explorations 