/// <summary>
/// Метод Хорд
/// </summary>
/// <param name="Function"></param>
/// <param name="X0">x(n)</param>
/// <param name="XLast">x(n-1) - not changed</param>
/// <param name="Epsilon"></param>
/// <returns>x(n+1)=y</returns>
public double ChordMethod(string Function, double X0, double XLast, double Epsilon, ref string resultTEXT)
{
double y = X0 -
(X0 - XLast) * CalcMethods.ParseFunction(Function, X0) /
(CalcMethods.DerivativeOfFunction(Function, X0) -
CalcMethods.DerivativeOfFunction(Function, XLast));
double k = 1;
resultTEXT = "Функция x = f(x) = " + Function + "\n";
resultTEXT += "x0 = " + X0 + " X1 = " + XLast + " Epsilon = " + Epsilon + "\n";
while ((Math.Abs(y - X0) > Epsilon))
{
resultTEXT += "\n|у -x0| = " + (Math.Abs(y - X0));
if (k > 500)
{
throw new ArgumentException("k > 500");
}
resultTEXT += "\n y = " + y;
resultTEXT += "\n k =" + k + "\n";
k++;
X0 = y;
y = X0 -
(X0 - XLast) * CalcMethods.ParseFunction(Function, X0) /
(CalcMethods.DerivativeOfFunction(Function, X0) - CalcMethods.DerivativeOfFunction(Function, XLast));
}
resultTEXT += "Результат =" + y + "\n";
return(y);
}
/// <summary>
/// Метод средних прямоугольников
/// </summary>
/// <param name="function">подинтегральная функция</param>
/// <param name="a">начало отрезка</param>
/// <param name="b">конец отрезка</param>
/// <param name="n">количество разбиений</param>
/// <returns></returns>
public double MidleRectangles(string function, double a, double b, int n)
{
double S = 0;
double h = (b - a) / n;
for (int i = 0; i < n; i++)
{
S = S + h * (CalcMethods.ParseFunction(function, (a + (i + 0.5) * h)));
}
return(S);
}
/// <summary>
/// метод левых прямоугольников
/// </summary>
/// <param name="function">подинтегральная функция</param>
/// <param name="a">начало отрезка [a, b]</param>
/// <param name="b">конец отрезка [a, b]</param>
/// <param name="n">количество разбиений отрезка</param>
/// <returns></returns>
public double LeftRectangles(string function, double a, double b, int n)
{
double S = 0;
double h = (b - a) / n;
for (int i = 1; i <= n; i++)
{
S = S + h * (CalcMethods.ParseFunction(function, (a + i * h)));
}
return(S);
}
/// <summary>
/// метод трапеций
/// </summary>
/// <param name="function">подинтегральная функция</param>
/// <param name="a">начало отрезка [a, b]</param>
/// <param name="b">конец отрезка [a, b]</param>
/// <returns></returns>
public double MethodOfTrapezoids(string function, double a, double b, int n)
{
double S = 0;
double h = (b - a) / n;
double x = a;
for (double i = 0; i < n + 1; i++)
{
if (i == 0 || i == n)
{
S = S + ((CalcMethods.ParseFunction(function, (x + i * h)))) * h / 2;
}
else
{
S = S + ((CalcMethods.ParseFunction(function, (x + i * h)))) * h;
}
}
return(S);
}
/// <summary>
/// метод 3/8
/// </summary>
/// <param name="function">подинтегральная функция</param>
/// <param name="a">начало отрезка [a, b]</param>
/// <param name="b">конец отрезка [a, b]</param>
/// <returns></returns>
public double Method_3_8(string function, double a, double b, int n)
{
double h = (b - a) / (3 * n);
double S = CalcMethods.ParseFunction(function, a) + CalcMethods.ParseFunction(function, b);
int m = 3 * n - 1;
double x;
for (int i = 1; i <= m; i++)
{
x = a + h * i;
if (i % 3 == 0)
{
S = S + 2 * CalcMethods.ParseFunction(function, x);
}
else
{
S = S + 3 * CalcMethods.ParseFunction(function, x);
}
}
return(S * 3 / 8 * h);
}
/// <summary>
/// метед простой итерации
/// </summary>
/// <param name="Function">искомая функция</param>
/// <param name="X0">начальное приближение</param>
/// <param name="Epsilon">точность вычисления</param>
/// <param name="resultTEXT"></param>
/// <returns></returns>
public double MethodOfSimpleIteration(string Function, double X0, double Epsilon, ref string resultTEXT)
{
double y = CalcMethods.ParseFunction(Function, X0);
double k = 1;
resultTEXT = "Функция x = f(x) = " + Function + "\n";
resultTEXT += "x0 = " + X0 + " Epsilon = " + Epsilon + "\n";
while ((Math.Abs(y - X0) > Epsilon))
{
resultTEXT += "\n|у -x0| = " + (Math.Abs(y - X0));
if (k > 500)
{
throw new ArgumentException("k > 500");
}
resultTEXT += "\n y = " + y;
resultTEXT += "\n k =" + k + "\n";
k++;
X0 = y;
y = CalcMethods.ParseFunction(Function, X0);
}
resultTEXT += "Результат =" + X0 + "\n";
return(y);
}
/// <summary>
/// метод парабол/симпсона
/// </summary>
/// <param name="function">подинтегральная функция</param>
/// <param name="a">начало отрезка [a, b]</param>
/// <param name="b">конец отрезка [a, b]</param>
/// <returns></returns>
public double MethodSimpsona(string function, double a, double b, int n)
{
double S = 0;
double h = (b - a) / n;
for (int i = 0; i <= n; i++)
{
if (i == 0 || i == n)
{
S = S + ((CalcMethods.ParseFunction(function, (a + i * h)))) * h / 2;
}
else
if (i % 2 == 0)
{
S = S + (2 * CalcMethods.ParseFunction(function, (a + i * h))) * h / 3;
}
else
{
S = S + (4 * CalcMethods.ParseFunction(function, (a + i * h))) * h / 3;
}
}
return(S);
}