Численные методы

Hide()
End Sub
End Class

Форма 3
Imports System.Math
Public Class Form3
Function Func(ByVal xp As Single) As Double
Dim n As Integer, Nn As Integer, i As Integer
Dim tmin As Double, tmax As Double, f0 As Double, fN As Double
Dim dt As Double, t(300) As Double, pi As Double

pi = 3.1415926535
n = 200
Nn = CInt(n / 2)
tmin = 0.0
tmax = xp
dt = (tmax - tmin) / (n - 1)
For i = 1 To n
t(i) = tmin + (i - 1) * dt
Next i
f0 = Exp(-tmin * tmin)
fN = Exp(-tmax * tmax)
Func = f0 + fN
For i = 1 To Nn - 1
Func = Func + 2 * Exp(-t(2 * i) * t(2 * i))
Next i
For i = 1 To Nn
Func = Func + 4 * Exp(-t(2 * i - 1) * t(2 * i - 1))
Next i
Func = dt * Func / 3
Func = 2 * Func / Sqrt(pi)
Func = Func + Exp(-xp * xp)
End Function
Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click
Dim a As Single, b As Single, eps As Single
Dim GoldenRatio As Single, ai As Single, bi As Single, xmax As Single
Dim x1 As Single, x2 As Single, f1 As Single, f2 As Single, epsi As Single
Dim i As Integer
Dim pi As Single

ListBox1.Items.Clear() : ListBox2.Items.Clear()
ListBox3.Items.Clear() : ListBox4.Items.Clear()
ListBox5.Items.Clear() : ListBox6.Items.Clear()
ListBox7.Items.Clear() : ListBox8.Items.Clear()

pi = 3.1415926535
'Значения входных параметров:
a = CSng(TextBox1.Text)
b = CSng(TextBox2.Text)
eps = CSng(TextBox3.Text)

GoldenRatio = CSng(0.5 * (1 + Sqrt(5)))
ai = a
bi = b
epsi = Abs(bi - ai)
i = 1
Do Until epsi < eps
x1 = bi - (bi - ai) / GoldenRatio
x2 = ai + (bi - ai) / GoldenRatio
f1 = CSng(Func(x1))
f2 = CSng(Func(x2))
If f1 <= f2 Then
ai = x1
Else
bi = x2
End If
epsi = Abs(bi - ai)
ListBox1.Items.Add(i)
ListBox2.Items.Add(Format(ai, "0.000000"))
ListBox3.Items.Add(Format(bi, "0.000000"))
ListBox4.Items.Add(Format(x1, "0.000000"))
ListBox5.Items.Add(Format(x2, "0.000000"))
ListBox6.Items.Add(Format(f1, "0.000000"))
ListBox7.Items.Add(Format(f2, "0.000000"))
ListBox8.Items.Add(Format(epsi, "0.000000"))
i = i + 1
Loop
xmax = CSng(0.5 * (ai + bi))

TextBox4.Text = Format(xmax, "0.000000")
TextBox5.Text = Format(Func(xmax), "0.000000")
End Sub
Private Sub Button2_Click(sender As Object, e As EventArgs) Handles Button2.Click
TextBox1.Text = "" : TextBox2.Text = "" : TextBox3.Text = ""
TextBox4.Text = "" : TextBox5.Text = ""
ListBox1.Items.Clear() : ListBox2.Items.Clear()
ListBox3.Items.Clear() : ListBox4.Items.Clear()
ListBox5.Items.Clear() : ListBox6.Items.Clear()
ListBox7.Items.Clear() : ListBox8.Items.Clear()
Me.Hide()
End Sub
End Class




Литература

Н.С. Бахвалов. Численные методы. М.: Наука, 1975.
Б.П. Демидович, И.А. Марон. Основы вычислительной математики. М.: ФМ, 1963.
А.А. Самарский, А.В. Гулин. Численные методы. М.: Наука, 1989.
В.Д. Колдаев. Численные методы и программирование. М.: ФОРУМ–ИНФРА-М, 2009.
А.В. Зенков. Численные методы: учеб. пособие. Екатеринбург: Изд. Ур. ун-та, 2016.













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Конец

Выходные данные:
Simpson

Simpson = h*Simpson/3

Simpson = Simpson + 4*Func(x(2*i-1))


i = 1,Nn

Simpson = Simpson + 2*Func(x(2*i))

i = 1,Nn-1

Nn = n/2
h = (b-a)/(Nn-1)
Simpson = Func(a) + Func(b)

Входные данные:
a, b, n

Начало








































Конец

Выходные данные:
xmax, Func(xmax)

xmax = 0.5*(a + b)

i = i + 1

Вывод:
i, a, b, x1, x2, f1, f2, Abs(b-a)

b = x2

a = x1

f1 <= f2

да

нет

x1 = b - (b - a)/GoldenRatio
x2 = a + (b - a)/GoldenRatio
f1 = Func(x1)
f2 = Func(x2)

нет

Abs(b-a) < eps

да

GoldenRatio = 0.5 * (1 + Sqrt(5))
i = 1

Входные данные:
a, b, eps

Начало




































































































Начало


Закрыть

Form1


График

Оптимизация

Close

Close


GoldenRatio

Graph


Form3

Form2

Конец