private static void test05()
//****************************************************************************80
//
// Purpose:
//
// TEST05 tests DIFFER_STENCIL.
//
// Discussion:
//
// Evaluate the coefficients for uniformly spaced finite difference
// approximations of derivatives.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 11 November 2013
//
// Author:
//
// John Burkardt
//
{
int i;
Console.WriteLine("");
Console.WriteLine("TEST05");
Console.WriteLine(" DIFFER_STENCIL produces coefficients for difference");
Console.WriteLine(" approximations of the O-th derivative,");
Console.WriteLine(" using arbitrarily spaced data, with maximum spacing H");
Console.WriteLine(" with error of order H^P.");
//
// Let X0 = 1.0.
//
double x0 = 0.0;
double h = 1.0;
Console.WriteLine("");
Console.WriteLine(" Use a spacing of H = " + h + " for all examples.");
//
// Forward difference approximation to the third derivative with error of O(h).
//
int o = 3;
int p = 1;
int n = o + p;
double[] c = new double[n];
double[] x = new double[n];
for (i = 0; i < n; i++)
{
x[i] = i * h;
}
Differ.differ_stencil(x0, o, p, x, ref c);
string label = " Forward difference coefficients, O = " + o.ToString()
+ ", P = " + p.ToString();
typeMethods.r8vec2_print(n, x, c, label);
//
// Backward difference approximation to the third derivative with error of O(h).
//
o = 3;
p = 1;
n = o + p;
c = new double[n];
x = new double[n];
for (i = 0; i < n; i++)
{
x[i] = (i + 1 - n) * h;
}
Differ.differ_stencil(x0, o, p, x, ref c);
label = " Backward difference coefficients, O = " + o.ToString()
+ ", P = " + p.ToString();
typeMethods.r8vec2_print(n, x, c, label);
//
// Central difference approximation to the third derivative with error of O(h^2).
//
o = 3;
p = 2;
n = o + p;
c = new double[n];
x = new double[n];
for (i = 0; i < n; i++)
{
x[i] = (-n + 1 + 2 * i) * h / 2.0;
}
Differ.differ_stencil(x0, o, p, x, ref c);
label = " Central difference coefficients, O = " + o.ToString()
+ ", P = " + p.ToString();
typeMethods.r8vec2_print(n, x, c, label);
//
// Central difference approximation to the third derivative with error of O(h^4).
//
o = 3;
p = 4;
n = o + p;
c = new double[n];
x = new double[n];
for (i = 0; i < n; i++)
{
x[i] = (-n + 1 + 2 * i) * h / 2.0;
}
Differ.differ_stencil(x0, o, p, x, ref c);
label = " Central difference coefficients, O = " + o.ToString()
+ ", P = " + p.ToString();
typeMethods.r8vec2_print(n, x, c, label);
//
// Forward difference approximation to the fourth derivative with error of O(h).
//
o = 4;
p = 1;
n = o + p;
c = new double[n];
x = new double[n];
for (i = 0; i < n; i++)
{
x[i] = i * h;
}
Differ.differ_stencil(x0, o, p, x, ref c);
label = " Forward difference coefficients, O = " + o.ToString()
+ ", P = " + p.ToString();
typeMethods.r8vec2_print(n, x, c, label);
//
// Backward difference approximation to the fourth derivative with error of O(h).
//
o = 4;
p = 1;
n = o + p;
c = new double[n];
x = new double[n];
for (i = 0; i < n; i++)
{
x[i] = (i + 1 - n) * h;
}
Differ.differ_stencil(x0, o, p, x, ref c);
label = " Backward difference coefficients, O = " + o.ToString()
+ ", P = " + p.ToString();
typeMethods.r8vec2_print(n, x, c, label);
//
// Central difference approximation to the fourth derivative with error of O(h^3).
//
o = 4;
p = 3;
n = o + p;
c = new double[n];
x = new double[n];
for (i = 0; i < n; i++)
{
x[i] = (-n + 1 + 2 * i) * h / 2.0;
}
Differ.differ_stencil(x0, o, p, x, ref c);
label = " Central difference coefficients, O = " + o.ToString()
+ ", P = " + p.ToString();
typeMethods.r8vec2_print(n, x, c, label);
}
