public static List <double> RungeKut(Math.Interval interval, FuncDiff func, double y0)
{
if (!interval.isValid)
{
return(null);
}
double deltaY, yNext, yPrev;
List <double> result = new List <double>();
yPrev = y0;
double k1, k2, k3, k4;
foreach (double x in interval.Points)
{
k1 = interval.Step * func(x, y0);
k2 = interval.Step * func(x + (interval.Step / 2), y0 + (k1 / 2));
k3 = interval.Step * func(x + (interval.Step / 2), y0 + (k2 / 2));
k4 = interval.Step * func(x + interval.Step, y0 + k3);
deltaY = (k1 + 2 * k2 + 2 * k3 + k4);
deltaY /= 6;
yNext = y0 + deltaY;
result.Add(y0);
y0 = yNext;
}
return(result);
}
public static double Simpson(Func func, Math.Interval interval)
{
if (!interval.isValid)
{
return(double.NaN);
}
if (interval.PointsCount % 2 == 0)
{
interval.PointsCount += 1;
}
double result = func(interval.A) + func(interval.B);
List <double> x = interval.Points;
double tmp1 = 0;
double tmp2 = 0;
for (int i = 1; i < x.Count - 1; i++)
{
if (i % 2 != 0)
{
tmp1 += func(x[i]);
}
else
{
tmp2 += func(x[i]);
}
}
result += 4 * tmp1 + 2 * tmp2;
return(result * interval.Step / 3);
}
public static double Iteration(Func polynom, Func dx, Math.Interval interval, double accuracy)
{
double xk = interval.A;
double x;
double dxMin, dxMax;
double lyambda;
dxMin = dxMax = dx(interval.A);
for (double i = interval.A; i < interval.B; i += accuracy)
{
if (dxMin > dx(i))
{
dxMin = dx(i);
}
if (dxMax < dx(i))
{
dxMax = dx(i);
}
}
if (dxMax <= 3 * dxMin)
{
lyambda = 1.25 / dxMax;
}
else
{
lyambda = 1 / dxMax;
}
do
{
x = xk;
xk = x - lyambda * polynom(x);
}while (Math.Abs(x - xk) >= accuracy);
return(xk);
}
public static List <double> EilerPlus(ref Math.Interval interval, FuncDiff func, double y0)
{
if (!interval.isValid)
{
return(null);
}
double deltaY, yNext, yPrev;
List <double> result = new List <double>();
yPrev = y0;
bool parity = true;
interval.PointsCount = interval.PointsCount * 2 - 1;
foreach (double x in interval.Points)
{
if (parity)
{
deltaY = interval.Step * func(x, y0);
yNext = y0 + deltaY;
}
else
{
deltaY = 2 * interval.Step * func(x, y0);
yNext = yPrev + deltaY;
}
result.Add(y0);
yPrev = y0;
y0 = yNext;
parity = !parity;
}
return(result);
}
private void DrawChart(Math.Interval interval, double step)
{
if (!interval.isValid)
{
return;
}
chPolindrome.Series[0].Points.Clear();
for (double i = interval.A; i <= interval.B + step; i += step)
{
chPolindrome.Series[0].Points.AddXY(i, Polindrome(i));
}
}
public Form1()
{
InitializeComponent();
chartInterval = new Math.Interval(-2, 2);
rootInterval = new Math.Interval(-2, 2);
tbA.Text = (-2).ToString();
tbB.Text = (2).ToString();
tbRootA.Text = (-2).ToString();
tbRootB.Text = (2).ToString();
rootAccuracy = 0.001;
tbRootAccuracy.Text = rootAccuracy.ToString();
}
public static double Rectangle(Func func, Math.Interval interval)
{
if (!interval.isValid)
{
return(double.NaN);
}
double result = 0;
List <double> x = interval.Points;
for (int i = 0; i < x.Count - 1; i++)
{
result += func(x[i] + interval.Step * 0.5);
}
return(result * interval.Step);
}
public static double Trapezoid(Func func, Math.Interval interval)
{
if (!interval.isValid)
{
return(double.NaN);
}
double result = (func(interval.A) + func(interval.B)) / 2;
List <double> x = interval.Points;
for (int i = 1; i < x.Count - 1; i++)
{
result += func(x[i]);
}
return(result * interval.Step);
}
public static List <double> Eiler(Math.Interval interval, FuncDiff func, double y0)
{
if (!interval.isValid)
{
return(null);
}
double deltaY, yNext;
List <double> result = new List <double>();
foreach (double x in interval.Points)
{
deltaY = interval.Step * func(x, y0);
yNext = y0 + deltaY;
result.Add(y0);
y0 = yNext;
}
return(result);
}
public bool Verification(Func polynom, Math.Interval interval, Label tbResult)
{
if (polynom(interval.A) == 0)
{
tbResult.Text = interval.A.ToString();
return(false);
}
if (polynom(interval.B) == 0)
{
tbResult.Text = interval.B.ToString();
return(false);
}
if (polynom(interval.A) * polynom(interval.B) > 0)
{
tbResult.Text = "Нет корня";
return(false);
}
if (!interval.isValid)
{
tbResult.Text = "Неверно указан интервал";
return(false);
}
return(true);
}
private void pbEilerPlus_Click(object sender, EventArgs e)
{
Math.Interval interval = ReadParametrs();
if (!interval.isValid)
{
return;
}
double y0;
if (!double.TryParse(tbY0.Text, out y0))
{
MessageBox.Show("Неверно указана начальная точка");
}
List <double> solution = DiffEq.EilerPlus(ref interval, DiffEqFunc, y0);
if (solution == null)
{
MessageBox.Show("Произошла ошибка");
}
FillDGV(interval.Points, solution, dgvResult);
}
public static double Dichotomy(Func polynom, Math.Interval interval, double accuracy)
{
double root, funcVal;
do
{
root = (interval.A + interval.B) / 2;
funcVal = polynom(root);
if (funcVal == 0)
{
break;
}
if (polynom(interval.A) * funcVal < 0)
{
interval.B = root;
}
else
{
interval.A = root;
}
} while (Math.Abs(interval.A - interval.B) >= accuracy);
return(root);
}
public static double Tangent(Func polynom, Func dx, Func d2x, Math.Interval interval, double accuracy)
{
double point, root;
if (polynom(interval.A) * d2x(interval.A) > 0)
{
do
{
point = interval.A;
interval.A = point - polynom(point) / dx(point);
root = interval.A;
}while (Math.Abs(interval.A - point) >= accuracy);
}
else
{
do
{
point = interval.B;
interval.B = point - polynom(point) / dx(point);
root = interval.B;
}while (Math.Abs(interval.B - point) >= accuracy);
}
return(root);
}
public static double Hords(Func polynom, Func d2x, Math.Interval interval, double accuracy)
{
double border, root;
if (d2x(interval.A) * polynom(interval.A) > 0)
{
do
{
border = interval.B;
interval.B = interval.B - ((interval.B - interval.A) * polynom(interval.B)) / (polynom(interval.B) - polynom(interval.A));
root = interval.B;
} while (Math.Abs(interval.B - border) >= accuracy);
}
else
{
do
{
border = interval.A;
interval.A = interval.A - ((interval.B - interval.A) * polynom(interval.A)) / (polynom(interval.B) - polynom(interval.A));
root = interval.A;
} while (Math.Abs(interval.A - border) >= accuracy);
}
return(root);
}