Método Numérico de Steffensen Calculado con Macros VBA de Excel

1. Cálculo de la raíz de una ecuación no lineal mediante el Método Numérico de Steffensen
Utilizando macros de VBA de Excel
Ing. Néstor Augusto Oyarce Linares
naoyarcel@gmail.com

2. aSteffensenGrafica - 1
Option Explicit
Sub XY_12_Dic_2020_7()
Dim X As Double, Y As Double, i As Integer, X1 As Double, X0 As Double, XX As Double
Dim Err As Double, YD As Double, j As Integer, gx0 As Double, gx As Double
'Método Numérico de STEFFENSEN
'14 de Diciembre de 2020, ejercicio 7
Cells.Clear
Cells(1, 1).Value = " ECUACION : "
Cells(3, 1).Value = " X^3+2*X^2+10*X-20"
Cells(1, 2).Value = " ENSAYOS : "
Cells(3, 2).Value = " X "
Cells(3, 3).Value = " Y "
For i = 1 To 10
X = 1 + i / 10
Y = (X) ^ (3) + 2 * (X) ^ (2) + 10 * X - 20
Cells(i + 3, 2).Value = X
Cells(i + 3, 3).Value = Y
If Y > 0 Then Exit For
Next i
Range("A1", "A3").Font.Bold = True
Cells.EntireColumn.AutoFit
End Sub
Sub Crea_grafico()
Dim grafico As ChartObject
Dim wks As Worksheet
Set wks = ActiveWorkbook.Sheets("Hoja1")
Set grafico = wks.ChartObjects.Add(Left:=400, Width:=450, Top:=50, Height:=200)
grafico.Name = "Grafico_1"
grafico.Chart.ChartType = xlXYScatterSmoothNoMarkers
grafico.Chart.SetSourceData Source:=wks.Range("B4:D15")
End Sub
' Ing. Néstor Augusto Oyarce Linares

3. ECUACION : ENSAYOS :
X^3+2*X^2+10*X-20 X Y
1.1 -5.249
1.2 -3.392
1.3 -1.423
1.4 0.664
-6
-5
-4
-3
-2
-1
0
1
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Series1
Series2

4. bSteffensenCalculo - 1
Option Explicit
Sub Parte2_Steffensen()
Dim X1 As Double, Y1 As Double, i As Integer, X2 As Double, Z As Double, Yb As Double
Dim Err As Double, Yz As Double, j As Integer, Y As Double, X As Double
'Función de Recurrencia de Steffensen
'X2 = X1 - (Y1)^2/(Yz-Y1)
'Z = X1+Y1
'Yz = f(Z)
Cells.Clear
Cells(1, 1).Value = "Método Numérico de Steffensen"
Cells(3, 2).Value = "Valor de X"
Cells(3, 3).Value = "Valor de Y"
Cells(3, 7).Value = "Iteraciones"
Cells(j + 3, 2).Value = " Xf "
Cells(j + 3, 3).Value = " Yf "
X1 = 1.3
For j = 1 To 20
Y1 = (X1) ^ (3) + 2 * (X1) ^ (2) + 10 * X1 - 20
Z = X1 + Y1
Yz = (Z) ^ (3) + 2 * (Z) ^ (2) + 10 * Z - 20
X2 = X1 - (Y1) ^ 2 / (Yz - Y1)
Y = (X2) ^ (3) + 2 * (X2) ^ (2) + 10 * X2 - 20
Err = Abs(X2 - X1)
Cells(j + 3, 2).Value = X2
Cells(j + 3, 3).Value = Y
If Err <= 0.0000001 Then Exit For
X1 = X2
Next j
X = X2
Y = (X) ^ (3) + 2 * (X) ^ (2) + 10 * X - 20
Cells(4, 5).Value = X
Cells(4, 6).Value = Y
Cells(4, 7).Value = j
Range("E1", "E4").Font.Bold = True
Range("E1", "E4").Font.Color = RGB(8, 44, 196)
Cells.EntireColumn.AutoFit
End Sub
' Ing. Néstor Augusto Oyarce Linares

5. Método Numérico de Steffensen
Xf Yf Iteraciones
1.402379779 0.71515279 1.368808108 2.22045E-15 6
1.375352109 0.138314932
1.369077229 0.005677868
1.368808571 9.76547E-06
1.368808108 2.89133E-11
1.368808108 2.22045E-15