Newton Repshons Method
Private Sub NewtonRapshon_Click()
ActiveSheet.Cells.Clear
Dim MaxIter As Integer
Dim MaxErr As Double
Dim x0 As Double
Dim NumIter As Integer
Dim err As Double
Dim xold As Double
Dim xnew As Double
Dim fold As Double
Dim dfold As Double
x0 = InputBox("Initial guess ")
Cells(1, 1).Value = "Initial guess "
Cells(1, 2).Value = x0
MaxErr = InputBox("Enter maximum % error")
Cells(2, 1).Value = "Maximum % error "
Cells(2, 2).Value = MaxErr
MaxIter = InputBox("Enter maximum number of iterations")
Cells(3, 1).Value = "Maximum number of iterations "
Cells(3, 2).Value = MaxIter
Cells(5, 1).Value = "Iter No"
Cells(5, 2).Value = "x"
Cells(5, 3).Value = "% error"
xold = x0
err = MaxErr + 0.001
NumIter = 0
Do While ((NumIter < MaxIter) And (err > MaxErr))
fold = Cos(xold) - xold ^ 3
dfold = -Sin(xold) - 3 * (xold ^ 2)
xnew = xold - (fold / dfold)
err = Abs(1 - xnew / xold) * 100
NumIter = NumIter + 1
Cells(NumIter + 5, 1).Value = NumIter
Cells(NumIter + 5, 2).Value = xnew
Cells(NumIter + 5, 3).Value = err
xold = xnew
Loop
End Sub
Public Function NewtonRapshon() As Variant()
Dim temp() As Variant
Dim MaxIter As Integer
Dim MaxErr As Double
Dim x0 As Double
Dim NumIter As Integer
Dim err As Double
Dim xold As Double
Dim xnew As Double
Dim fold As Double
Dim dfold As Double
x0 = InputBox("Initial guess ")
MaxErr = InputBox("Enter maximum % error")
MaxIter = InputBox("Enter maximum number of iterations")
ReDim temp(1 To MaxIter + 1, 1 To 3)
xold = x0
err = MaxErr + 0.001
NumIter = 0
temp(NumIter + 1, 1) = " Iteration "
temp(NumIter + 1, 2) = " Error "
temp(NumIter + 1, 3) = " Root "
Do While ((NumIter < MaxIter) And (err > MaxErr))
fold = Cos(xold) - xold ^ 3
dfold = -Sin(xold) - 3 * (xold ^ 2)
xnew = xold - (fold / dfold)
err = Abs(1 - xnew / xold) * 100
NumIter = NumIter + 1
xold = xnew
temp(NumIter + 1, 1) = NumIter
temp(NumIter + 1, 2) = err
temp(NumIter + 1, 3) = xnew
Loop
NewtonRapshon = temp
End Function
Private Sub CommandButton1_Click()
Dim emptyRow As Long
'Make Sheet1 active
Sheet1.Activate
'Determine emptyRow
emptyRow = WorksheetFunction.CountA(Range("A:A")) + 1
ActiveSheet.Cells.Clear
Dim MaxIter As Integer
Dim MaxErr As Double
Dim x0 As Double
'Transfer information
x0 = TextBoxX0.Value
MaxErr = TextBoxMaxErr.Value
MaxIter = TextBoxMaxIter.Value
Dim NumIter As Integer
Dim err As Double
Dim xold As Double
Dim xnew As Double
Dim fold As Double
Dim dfold As Double
Cells(1, 1).Value = "Initial guess "
Cells(1, 2).Value = x0
Cells(2, 1).Value = "Maximum % error "
Cells(2, 2).Value = MaxErr
Cells(3, 1).Value = "Maximum number of iterations "
Cells(3, 2).Value = MaxIter
Cells(5, 1).Value = "Iter No"
Cells(5, 2).Value = "x"
Cells(5, 3).Value = "% error"
xold = x0
err = MaxErr + 0.001
NumIter = 0
Do While ((NumIter < MaxIter) And (err > MaxErr))
fold = Cos(xold) - xold ^ 3
dfold = -Sin(xold) - 3 * (xold ^ 2)
xnew = xold - (fold / dfold)
err = Abs(1 - xnew / xold) * 100
NumIter = NumIter + 1
Cells(NumIter + 5, 1).Value = NumIter
Cells(NumIter + 5, 2).Value = xnew
Cells(NumIter + 5, 3).Value = err
xold = xnew
Loop
LabelRoot.Caption = CStr(xnew)
LabelError.Caption = CStr(err)
Dim ws As Worksheet
Dim rngData1, rngData2 As Range
Dim cht1, cht2 As Chart
Dim chtObj1, chtObj2 As ChartObject
Dim startCell As Range
Dim endCell As Range
'Define the worksheet and data range for the chart
Set ws = ThisWorkbook.Sheets("Sheet1") ' Change "Sheet1" to your actual sheet name
' Define the start and end cells using row and column numbers (e.g., A1 and C5)
Set startCell = ws.Cells(6, 2)
Set endCell = ws.Cells(NumIter + 5, 2)
' Use the Range property with the two cell references
Set rngData1 = ws.Range(startCell, endCell)
Set chtObj1 = ws.ChartObjects.Add(Left:=200, Top:=200, Width:=200, Height:=200)
' Get the Chart object from the ChartObject
Set cht1 = chtObj1.Chart
cht1.ChartType = xlLine
cht1.SetSourceData Source:=rngData1
Set startCell = ws.Cells(6, 3)
Set endCell = ws.Cells(NumIter + 5, 3)
' Use the Range property with the two cell references
Set rngData2 = ws.Range(startCell, endCell)
Set chtObj2 = ws.ChartObjects.Add(Left:=500, Top:=200, Width:=200, Height:=200)
' Get the Chart object from the ChartObject
Set cht2 = chtObj2.Chart
cht2.ChartType = xlLine
cht2.SetSourceData Source:=rngData2
End Sub
Private Sub UserForm_Initialize()
TextBoxX0.Value = ""
TextBoxX0.SetFocus
'Empty all other text box fields
TextBoxMaxErr.Value = ""
TextBoxMaxIter.Value = ""
End Sub
Bisection Method
Private Sub Bisection_Click()
Dim a As Double, b As Double, c As Double, d As Double
Dim fa As Double, fb As Double, fc As Double
Dim MaxIter As Integer, NumIter As Integer
Dim Tol As Double
a = InputBox("Enter the lower bound 'a':")
Cells(1, 1).Value = "Lower bound value, a"
Cells(1, 2).Value = a
b = InputBox("Enter the upper bound 'b':")
Cells(2, 1).Value = "Upper bound value, b"
Cells(2, 2).Value = b
Tol = InputBox("Enter the tolerance:")
Cells(3, 1).Value = "Tolerance"
Cells(3, 2).Value = Tol
MaxIter = InputBox("Enter maximum number of iterations")
Cells(4, 1).Value = "Maximum number of iterations"
Cells(4, 2).Value = MaxIter
Cells(6, 1).Value = "Iter"
Cells(6, 2).Value = "a"
Cells(6, 3).Value = "b"
Cells(6, 4).Value = "c"
Cells(6, 5).Value = "fa"
Cells(6, 6).Value = "fc"
NumIter = 0
fa = a ^ 3 - 6 * (a ^ 2) + 11 * a - 6
fb = b ^ 3 - 6 * (b ^ 2) + 11 * b - 6
If fa * fb > 0 Then
MsgBox "Invalid interval!"
Exit Sub
End If
Do While NumIter < MaxIter
c = (a + b) / 2
fa = a ^ 3 - 6 * (a ^ 2) + 11 * a - 6
fc = c ^ 3 - 6 * (c ^ 2) + 11 * c - 6
d = b - a
NumIter = NumIter + 1
Cells(NumIter + 6, 1).Value = NumIter
Cells(NumIter + 6, 2).Value = a
Cells(NumIter + 6, 3).Value = b
Cells(NumIter + 6, 4).Value = c
Cells(NumIter + 6, 5).Value = fa
Cells(NumIter + 6, 6).Value = fc
If d < Tol Then
MsgBox "Root found: " & Round(c, 6)
Exit Sub
End If
If fa * fc < 0 Then
b = c
Else
a = c
End If
Loop
MsgBox "Max iterations reached. Root ˜ " & Round(c, 6)
End Sub
Public Function BisectionMethod()
Dim temp() As Variant
Dim MaxIter As Integer
Dim Tol As Double
Dim a As Double, b As Double, c As Double
Dim fa As Double, fb As Double, fc As Double
Dim NumIter As Integer
Dim d As Double
a = InputBox("Enter lower bound (a): ")
b = InputBox("Enter upper bound (b): ")
Tol = InputBox("Enter tolerance: ")
MaxIter = InputBox("Enter maximum number of iterations")
ReDim temp(1 To MaxIter + 1, 1 To 3)
NumIter = 0
temp(1, 1) = "Iteration"
temp(1, 2) = "Tolerance (b-a)"
temp(1, 3) = "Root"
fa = a ^ 3 - 6 * a ^ 2 + 11 * a - 6
fb = b ^ 3 - 6 * b ^ 2 + 11 * b - 6
If fa * fb > 0 Then
MsgBox "Invalid interval!"
Exit Function
End If
Do While NumIter < MaxIter
c = (a + b) / 2
fa = a ^ 3 - 6 * a ^ 2 + 11 * a - 6
fc = c ^ 3 - 6 * c ^ 2 + 11 * c - 6
d = b - a
NumIter = NumIter + 1
temp(NumIter + 1, 1) = NumIter
temp(NumIter + 1, 2) = d
temp(NumIter + 1, 3) = c
If d < Tol Then
Exit Do
End If
If fa * fc < 0 Then
b = c
Else
a = c
End If
Loop
BisectionMethod = temp
End Function
Private Sub BisectionButton_Click()
Dim a As Double, b As Double, c As Double
Dim fa As Double, fb As Double, fc As Double
Dim MaxIter As Integer, NumIter As Integer
Dim Tol As Double, tolVal As Double
Dim ws As Worksheet
Set ws = ThisWorkbook.Sheets("Sheet1")
' Clear sheet
ws.Cells.Clear
' Delete old charts
Dim obj As ChartObject
For Each obj In ws.ChartObjects
obj.Delete
Next obj
' ===== INPUTS =====
a = Val(TextBoxA.Value)
b = Val(TextBoxB.Value)
MaxIter = Val(TextBoxMaxIter.Value)
Tol = Val(TextBoxTol.Value)
' ===== HEADERS =====
ws.Cells(6, 1) = "Iter"
ws.Cells(6, 2) = "Root"
ws.Cells(6, 3) = "Tolerance"
NumIter = 0
' Initial function values
fa = a ^ 3 - 6 * a ^ 2 + 11 * a - 6
fb = b ^ 3 - 6 * b ^ 2 + 11 * b - 6
If fa * fb > 0 Then
MsgBox "Invalid interval!"
Exit Sub
End If
' ===== BISECTION LOOP =====
Do While NumIter < MaxIter
c = (a + b) / 2
fc = c ^ 3 - 6 * c ^ 2 + 11 * c - 6
tolVal = Abs(b - a)
NumIter = NumIter + 1
ws.Cells(NumIter + 6, 1) = NumIter
ws.Cells(NumIter + 6, 2) = c
ws.Cells(NumIter + 6, 3) = tolVal
If tolVal < Tol Then Exit Do
If fa * fc < 0 Then
b = c
Else
a = c
End If
Loop
' ===== OUTPUT =====
Label7.Caption = Round(c, 6)
Label9.Caption = tolVal
' =========================
' GRAPH 1: ROOT
' =========================
Dim chtObj1 As ChartObject
Set chtObj1 = ws.ChartObjects.Add(Left:=200, Top:=200, Width:=250, Height:=200)
With chtObj1.Chart
.ChartType = xlLine
.SeriesCollection.NewSeries
.SeriesCollection(1).XValues = ws.Range(ws.Cells(7, 1), ws.Cells(NumIter + 6, 1))
.SeriesCollection(1).Values = ws.Range(ws.Cells(7, 2), ws.Cells(NumIter + 6, 2))
.SeriesCollection(1).Name = "Root"
.HasTitle = True
.ChartTitle.Text = "Root Convergence"
.HasLegend = False
.Axes(xlCategory).HasTitle = True
.Axes(xlCategory).AxisTitle.Text = "Iteration"
.Axes(xlValue).HasTitle = True
.Axes(xlValue).AxisTitle.Text = "Root"
.Axes(xlCategory).TickLabelSpacing = 1
End With
' =========================
' GRAPH 2: TOLERANCE
' =========================
Dim chtObj2 As ChartObject
Set chtObj2 = ws.ChartObjects.Add(Left:=500, Top:=200, Width:=250, Height:=200)
With chtObj2.Chart
.ChartType = xlLine
.SeriesCollection.NewSeries
.SeriesCollection(1).XValues = ws.Range(ws.Cells(7, 1), ws.Cells(NumIter + 6, 1))
.SeriesCollection(1).Values = ws.Range(ws.Cells(7, 3), ws.Cells(NumIter + 6, 3))
.SeriesCollection(1).Name = "Tolerance"
.HasTitle = True
.ChartTitle.Text = "Tolerance Convergence"
.HasLegend = False
.Axes(xlCategory).HasTitle = True
.Axes(xlCategory).AxisTitle.Text = "Iteration"
.Axes(xlValue).HasTitle = True
.Axes(xlValue).AxisTitle.Text = "Tolerance"
.Axes(xlCategory).TickLabelSpacing = 1
End With
End Sub
