private MathFunction UK(BoundaryValueTask task, int k)
{
if (k == 0)
{
double[,] m = new double[, ]
{
{ task.alpha0 *task.a + task.alpha1, task.alpha0 },
{ task.betta0 *task.b + task.betta1, task.betta0 }
};
double[] v = new double[] { task.A, task.B };
Vector res = method.Solve(new SLAE(m, v));
return(new XFunction(res[0]) + res[1]);
}
return((new XFunction(1.0) ^ (k - 1)) *
(new XFunction(1.0) - task.a) * (new XFunction(1.0) - task.b));
}
public KeyValuePair <double, double>[] Solve(BoundaryValueTask task, int n)
{
MathFunction[] u = new MathFunction[collocationN + 1];
for (int i = 0; i <= collocationN; i++)
{
u[i] = UK(task, i);
}
double[,] matrix = new double[collocationN, collocationN];
double[] vect = new double[collocationN];
double h = (task.b - task.a) / (collocationN + 1);
for (int i = 0; i < collocationN; i++)
{
double xi = task.a + (i + 1) * h;
vect[i] = task.FX.Calculate(xi) - task.LOperator(u[0], xi);
for (int j = 0; j < collocationN; j++)
{
matrix[i, j] = task.LOperator(u[j + 1], xi);
}
}
Vector C = method.Solve(new SLAE(matrix, vect));
MathFunction yn = u[0];
yn.Calculate(0);
for (int i = 1; i <= collocationN; i++)
{
yn += C[i - 1] * u[i];
}
h = (task.b - task.a) / n;
KeyValuePair <double, double>[] result = new KeyValuePair <double, double> [n + 1];
for (int i = 0; i < result.Length; i++)
{
result[i] = new KeyValuePair <double, double>(task.a + i * h, yn.Calculate(task.a + i * h));
}
return(result);
}
public KeyValuePair <double, double>[] Solve(BoundaryValueTask task, int n)
{
double[,] matrix = new double[n + 1, n + 1];
double[] vect = new double[n + 1];
double h = (task.b - task.a) / n;
vect[0] = task.A * h;
vect[n] = task.B * h;
matrix[0, 0] = task.alpha0 * h - task.alpha1;
matrix[0, 1] = task.alpha1;
matrix[n, n] = task.betta0 * h + task.betta1;
matrix[n, n - 1] = -task.betta1;
for (int i = 1; i <= n - 1; i++)
{
double xi = task.a + i * h;
vect[i] = 2 * Math.Pow(h, 2) * task.FX.Calculate(xi);
matrix[i, i + 1] = 2 + task.PX.Calculate(xi) * h;
matrix[i, i] = task.QX.Calculate(xi) * 2 * Math.Pow(h, 2) - 4;
matrix[i, i - 1] = 2 - task.PX.Calculate(xi) * h;
}
Vector yx = new GaussMethod().Solve(new SLAE(matrix, vect));
KeyValuePair <double, double>[] result = new KeyValuePair <double, double> [yx.Count];
for (int i = 0; i < result.Length; i++)
{
result[i] = new KeyValuePair <double, double>(task.a + i * h, yx[i]);
}
return(result);
}