public Differential_Equation()
{
table1 = new Table();
table2 = new Table();
table3 = new Table();
double h_0 = h * F(x_0, y_0);
table1.Add(x_0, y_0, h_0);
table2.Add(x_0, y_0, h_0);
table3.Add(x_0, y_0, h_0);
}
public void Euler(int left, int right, Table table, double factor)
{
for (int i = left; i < factor * right + 1; i++)
euler_iter(i, ref table, factor);
}
public void Adams(int left, int right, Table table)
{
for (int i = left; i < right + 1; i++)
adams_iter(i, ref table);
}
private void runge_kutti(int i, ref Table table)
{
double x_prev = table.X(i - 1);
double y_prev = table.Y(i - 1);
double k1 = h * F(x_prev, y_prev);
double k2 = h * F(x_prev + h / 2.0, y_prev + k1 / 2.0);
double k3 = h * F(x_prev + h / 2.0, y_prev + k2 / 2.0);
double k4 = h * F(x_prev + h, y_prev + k3);
double x_next = x_prev + h;
double y_next = y_prev + (k1 + 2 * k2 + 2 * k3 + k4) / 6.0;
double hi_next = h * F(x_next, y_next);
table.Add(x_next, y_next, hi_next);
}
private void euler_iter(int i, ref Table table, double factor)
{
double x_prev, x_next, y_prev, y_next, hi_prev, hi_next;
double h = H / factor;
x_prev = table.X(i - 1);
y_prev = table.Y(i - 1);
hi_prev = table.Hi(0, i - 1);
x_next = x_prev + h;
y_next = y_prev + hi_prev;
hi_next = h * F(x_next, y_next);
table.Add(x_next, y_next, hi_next);
}
private void adams_iter(int i, ref Table table)
{
double x_prev = table.X(i - 1);
double y_prev = table.Y(i - 1);
double hi_prev = table.Hi(0, i - 1);
double delta_1_hi = table.Hi(1, i - 2);
double delta_2_hi = table.Hi(2, i - 3);
double delta_3_hi = table.Hi(3, i - 4);
double delta_4_hi = table.Hi(4, i - 5);
double x_next = x_prev + h;
double y_next = y_prev + hi_prev + delta_1_hi / 2.0 + 5.0 * delta_2_hi / 12.0 +
3.0 * delta_3_hi / 8.0 + 251.0 * delta_4_hi / 720.0;
double hi_next = h * F(x_next, y_next);
table.Add(x_next, y_next, hi_next);
}
public void RungeKutti(int left, int right, Table table)
{
for (int i = left; i < right + 1; i++)
runge_kutti(i, ref table);
}