private static void test04()
//****************************************************************************80
//
// Purpose:
//
// TEST04 tests DIFFER_FORWARD, DIFFER_BACKWARD, DIFFER_CENTRAL.
//
// 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
//
{
Console.WriteLine("");
Console.WriteLine("TEST04");
Console.WriteLine(" DIFFER_FORWARD,");
Console.WriteLine(" DIFFER_BACKWARD, and");
Console.WriteLine(" DIFFER_CENTRAL produce coefficients for difference");
Console.WriteLine(" approximations of the O-th derivative,");
Console.WriteLine(" with error of order H^P, for a uniform spacing of H.");
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];
Differ.differ_forward(h, o, p, ref c, ref x);
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];
Differ.differ_backward(h, o, p, ref c, ref x);
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];
Differ.differ_central(h, o, p, ref c, ref x);
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];
Differ.differ_central(h, o, p, ref c, ref x);
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];
Differ.differ_forward(h, o, p, ref c, ref x);
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];
Differ.differ_backward(h, o, p, ref c, ref x);
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];
Differ.differ_central(h, o, p, ref c, ref x);
label = " Central difference coefficients, O = " + o.ToString()
+ ", P = " + p.ToString();
typeMethods.r8vec2_print(n, x, c, label);
}