public static double[,] EulerIII(
double x0,
double y0,
double h,
int k,
int N,
ComputationalWorkShop.Function.G f)
{
var m = N - k + 1;
var table = new double[m + 1, 2];
table[0, 0] = x0;
table[0, 1] = y0;
var ytemp = 0.0;
for (int i = 1; i < m + 1; i++)
{
ytemp = table[i - 1, 1] +
(h *
f(table[i - 1, 0],
table[i - 1, 1]));
table[i, 0] = x0 + (i * h);
table[i, 1] = table[i - 1, 1] +
((h / 2) *
(f(table[i - 1, 0],
table[i - 1, 1]) +
f(table[i, 0],
ytemp)));
}
return(table);
}
public static double[,] Adams(
ComputationalWorkShop.Function.G f,
double[,] nodes,
double h,
int k,
int N)
{
int m0 = nodes.GetLength(0) - 1;
int m1 = N - k;
var table = new double[m0 + m1 + 2, 2];
for (int i = 0; i < m0 + 1; i++)
{
table[i, 0] = nodes[i, 0];
table[i, 1] = nodes[i, 1];
}
var etha = new double[m0 + m1 + 2, 5];
for (int i = 0; i < m0 + 1; i++)
{
etha[i, 0] = h * f(table[i, 0], table[i, 1]);
}
for (int j = 1; j < 5; j++)
{
for (int i = 0; i < 4 - j + 1; i++)
{
etha[i, j] = etha[i + 1, j - 1] - etha[i, j - 1];
}
}
var delta = 0.0;
for (int i = m0 + 1; i < m0 + m1 + 2; i++)
{
delta = etha[i - 1, 0] +
(1 / 2.0) * etha[i - 2, 1] +
(5 / 12.0) * etha[i - 3, 2] +
(3 / 8.0) * etha[i - 4, 3] +
(251 / 720.0) * etha[i - 5, 4];
table[i, 1] = table[i - 1, 1] + delta;
table[i, 0] = table[i - 1, 0] + h;
etha[i, 0] = h * f(table[i, 0], table[i, 1]);
for (int j = 1; j < m0 + 1; j++)
{
etha[i - j, j] = etha[i - j + 1, j - 1] -
etha[i - j, j - 1];
}
}
return(table);
}
public static double[,] RungeKutt(
double x0,
double y0,
double h,
int k,
int N,
ComputationalWorkShop.Function.G f)
{
var m = N - k + 1;
var table = new double[m + 1, 2];
table[0, 0] = x0;
table[0, 1] = y0;
var k1 = 0.0;
var k2 = 0.0;
var k3 = 0.0;
var k4 = 0.0;
for (int i = 1; i < m + 1; i++)
{
k1 = h * f(table[i - 1, 0], table[i - 1, 1]);
k2 = h *
f(table[i - 1, 0] +
(h / 2.0), table[i - 1, 1] +
(k1 / 2.0));
k3 = h *
f(table[i - 1, 0] +
(h / 2.0), table[i - 1, 1] +
(k2 / 2.0));
k4 = h *
f(table[i - 1, 0] + h,
table[i - 1, 1] + k3);
table[i, 0] = x0 + (i * h);
table[i, 1] = table[i - 1, 1] +
(1 / 6.0) *
(k1 + 2 *
(k2 + k3) + k4);
}
return(table);
}
