private static void fd1d_bvp_test01()
//****************************************************************************80
//
// Purpose:
//
// FD1D_BVP_TEST01 carries out test case #1.
//
// Discussion:
//
// Use A1, C1, F1, EXACT1.
//
// Repeat using a nonuniform mesh.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 15 February 2011
//
// Author:
//
// John Burkardt
//
{
int i;
const int n = 21;
const double x1 = 0.0;
const double x2 = 1.0;
Console.WriteLine("");
Console.WriteLine("FD1D_BVP_TEST01");
Console.WriteLine(" A1(X) = 1.0");
Console.WriteLine(" A1'(X) = 0.0");
Console.WriteLine(" C1(X) = 0.0");
Console.WriteLine(" F1(X) = X * ( X + 3 ) * exp ( X )");
Console.WriteLine(" U1(X) = X * ( 1 - X ) * exp ( X )");
Console.WriteLine("");
Console.WriteLine(" Number of nodes = " + n + "");
Console.WriteLine(" X1 = " + x1 + "");
Console.WriteLine(" X2 = " + x2 + "");
double[] x = typeMethods.r8vec_even(n, x1, x2);
double[] u = FDM_1D_BVP.fd1d_bvp(n, a1, a1prime, c1, f1, x);
double[] uexact = exact1(n, x);
Console.WriteLine("");
Console.WriteLine(" I X U Uexact Error");
Console.WriteLine("");
for (i = 0; i < n; i++)
{
Console.WriteLine(" " + i.ToString(CultureInfo.InvariantCulture).PadLeft(4)
+ " " + x[i].ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + u[i].ToString(CultureInfo.InvariantCulture).PadLeft(12)
+ " " + uexact[i].ToString(CultureInfo.InvariantCulture).PadLeft(12)
+ " " + Math.Abs(u[i] - uexact[i]).ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
Console.WriteLine("");
Console.WriteLine(" Repeat, using a nonuniform mesh.");
x = typeMethods.r8vec_even(n, x1, x2);
for (i = 0; i < n; i++)
{
x[i] = Math.Sqrt(x[i]);
}
u = FDM_1D_BVP.fd1d_bvp(n, a1, a1prime, c1, f1, x);
uexact = exact1(n, x);
Console.WriteLine("");
Console.WriteLine(" I X U Uexact Error");
Console.WriteLine("");
for (i = 0; i < n; i++)
{
Console.WriteLine(" " + i.ToString(CultureInfo.InvariantCulture).PadLeft(4)
+ " " + x[i].ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + u[i].ToString(CultureInfo.InvariantCulture).PadLeft(12)
+ " " + uexact[i].ToString(CultureInfo.InvariantCulture).PadLeft(12)
+ " " + Math.Abs(u[i] - uexact[i]).ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
//
// Write the data to files.
//
string filename = "fd1d_bvp_test01_nodes.txt";
typeMethods.r8mat_write(filename, n, 1, x);
double[] u2 = new double[n * 2];
for (i = 0; i < n; i++)
{
u2[i + 0 * n] = u[i];
}
for (i = 0; i < n; i++)
{
u2[i + 1 * n] = uexact[i];
}
filename = "fd1d_bvp_test01_values.txt";
typeMethods.r8mat_write(filename, n, 2, u2);
}
private static void fd1d_bvp_test05()
//****************************************************************************80
//
// Purpose:
//
// FD1D_BVP_TEST05 carries out test case #5.
//
// Discussion:
//
// Use A3, C1, F5, EXACT1.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 15 February 2011
//
// Author:
//
// John Burkardt
//
{
int i;
const int n = 11;
const double x1 = 0.0;
const double x2 = 1.0;
Console.WriteLine("");
Console.WriteLine("FD1D_BVP_TEST05");
Console.WriteLine(" A3(X) = 1.0 + X * X for X <= 1/3");
Console.WriteLine(" = 7/9 + X for 1/3 < X");
Console.WriteLine(" A3''(X) = 2.0 * X for X <= 1/3");
Console.WriteLine(" 1 for 1/3 < X");
Console.WriteLine(" C1(X) = 0.0");
Console.WriteLine(" F5(X) = ( X + 3 X^2 + 5 X^3 + X^4 ) * exp ( X )");
Console.WriteLine(" for X <= 1/3");
Console.WriteLine(" = ( - 1 + 10/3 X + 43/9 X^2 + X^3 ) * exp ( X )");
Console.WriteLine(" for 1/3 <= X");
Console.WriteLine(" U1(X) = X * ( 1 - X ) * exp ( X )");
Console.WriteLine("");
Console.WriteLine(" Number of nodes = " + n + "");
Console.WriteLine(" X1 = " + x1 + "");
Console.WriteLine(" X2 = " + x2 + "");
double[] x = typeMethods.r8vec_even(n, x1, x2);
double[] u = FDM_1D_BVP.fd1d_bvp(n, a3, a3prime, c1, f5, x);
double[] uexact = exact1(n, x);
Console.WriteLine("");
Console.WriteLine(" I X U Uexact Error");
Console.WriteLine("");
for (i = 0; i < n; i++)
{
Console.WriteLine(" " + i.ToString(CultureInfo.InvariantCulture).PadLeft(4)
+ " " + x[i].ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + u[i].ToString(CultureInfo.InvariantCulture).PadLeft(12)
+ " " + uexact[i].ToString(CultureInfo.InvariantCulture).PadLeft(12)
+ " " + Math.Abs(u[i] - uexact[i]).ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
//
// Write the data to files.
//
string filename = "fd1d_bvp_test05_nodes.txt";
typeMethods.r8mat_write(filename, n, 1, x);
double[] u2 = new double[n * 2];
for (i = 0; i < n; i++)
{
u2[i + 0 * n] = u[i];
}
for (i = 0; i < n; i++)
{
u2[i + 1 * n] = uexact[i];
}
filename = "fd1d_bvp_test05_values.txt";
typeMethods.r8mat_write(filename, n, 2, u2);
}
