public static double Simpsons(double a, double b, int m, int l, int k)
{
int m2 = m;
double[] x = new double[m + 1];
double h = (b - a) / m;
for (int i = 0; i <= m; ++i)
{
x[i] = a + i * h;
}
double jh = 0.0;
for (int i = 0; i < m; ++i)
{
MU f1 = new MU(x[i], k);
MU f2 = new MU(x[i] + h/2, k);
MU f3 = new MU(x[i + 1], k);
jh = jh + h / 6 * (f1.reVal() + 4 * f2.reVal() + f3.reVal());
}
m *= l;
x = new double[m + 1];
h = (b - a) / m;
for (int i = 0; i <= m; ++i)
{
x[i] = a + i * h;
}
double jh2 = 0.0;
for (int i = 0; i < m; ++i)
{
MU f1 = new MU(x[i], k);
MU f2 = new MU(x[i] + h / 2, k);
MU f3 = new MU(x[i + 1], k);
jh2 = jh2 + h / 6 * (f1.reVal() + 4 * f2.reVal() + f3.reVal());
}
Integral j = new Integral(b, a);
double rm=(jh2-jh)/(double)(Math.Pow(l,4) - 1);
return (jh2 + rm);
}
public static void KFormula(double a, double b, int n)
{
double[] mu = new double[2*n];
for (int i = 0; i < 2*n; ++i)
mu[i] = IntegralMu(a, b, i);
Console.WriteLine();
Console.WriteLine("Weight:");
for (int i = 0; i < 2 * n; ++i)
Console.Write("Mu{0}\t",i);
Console.WriteLine();
for (int i = 0; i < 2*n; ++i)
Console.Write("{0:f5} ", mu[i]);
Console.WriteLine();
int l;
Matrix m = new Matrix(n,n+1);
for (int i = 0; i < n; ++i)
{
l = i;
for (int j = n; j >=0; --j)
{
m[i, j] = mu[l];
++l;
}
}
m.SwapStolb(0, n);
Console.WriteLine();
Console.WriteLine("Matrix of the system to find the odds w(x):");
for (int i = 0; i < m.GetLength(0); ++i)
m[i, n] = -1 * m[i, n];
for (int i = 0; i <m.GetLength(0); ++i)
{
for (int j = 0; j < m.GetLength(1); ++j)
Console.Write("{0:f3} ",m[i, j]);
Console.WriteLine();
}
Console.WriteLine();
double[] c;
c = MethodKramera(m);
MethodBessekcii(a, b, c, n);
double[] node = new double[nodes.Count];
for (int i = 0; i < node.Length; ++i)
node[i] = nodes.Dequeue();
Console.WriteLine("The roots of the polynomial w (x) (future nodes):");
for (int i = 0; i < node.Length; ++i)
Console.WriteLine("X{0} = {1:f15}", i, node[i]);
if (node.Length != n)
{
Console.WriteLine("Error! Bisection method has found roots < n");
return;
}
m = new Matrix(n, n + 1);
for (int i = 0; i < m.GetLength(0); ++i)
for (int j = 0; j < m.GetLength(1); ++j)
if (j < n) m[i, j] = Math.Pow(node[j], i); else m[i, j] = mu[i];
Console.WriteLine();
Console.WriteLine("Matrix of the system to find the odds quadrature formula:");
for (int i = 0; i < m.GetLength(0); ++i)
{
for (int j = 0; j < m.GetLength(1); ++j)
Console.Write("{0:f3} ", m[i, j]);
Console.WriteLine();
}
Console.WriteLine();
c = MethodKramera(m);
Console.WriteLine("Coefficient of the quadrature formula:");
for (int i = 0; i < c.Length; ++i)
Console.WriteLine("A{0} = {1:f15} ",i+1, c[i]);
Console.WriteLine();
Fun f = new Fun(node);
double result=0.0;
Integral I=new Integral(b,a);
for (int i = 0; i < n; ++i)
result += f.reVal(i) * c[i];
Console.WriteLine("Checking:");
for (int i = 0; i < 2 * n; ++i)
{
double s=0;
for (int j = 0; j < n; ++j)
s+=c[j]*Math.Pow(node[j],i);
Console.WriteLine("Mu{0} = {1:f5} = {2:f5}", i, mu[i], s);
}
Console.WriteLine();
Console.WriteLine("Result:");
Console.WriteLine("J(h) = {0:f15}", result);
Console.WriteLine("J = {0:f15}", I.reVal());
Console.WriteLine("R = {0:f15}", Math.Abs(I.reVal() - result));
}