This document describes using Excel VBA macros to calculate the root of a non-linear equation using the Numerical False Position Method. It presents code to generate sample data for a cubic equation, plot the results on a graph, and implement the iterative false position method calculations to determine the root of the equation within a specified tolerance over multiple iterations.

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

2. aFalsaPosicionGrafica - 1
Option Explicit
Sub XY_10_Dic_2020_4()
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 FALSA POSICIÓN
'10 de Diciembre de 2020, ejercicio 4
Cells.Clear
Cells(1, 1).Value = " ECUACIÓN : "
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. ECUACIÓN : 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. bFalsaPosicionCalculo - 1
Option Explicit
Sub Parte2_Falsa_Posición()
Dim Xa As Double, Ya As Double, i As Integer, Xb As Double, Xm As Double, Yb As Double
Dim Error As Double, Ym As Double, j As Integer, X As Double, Y As Double
'Función de Recurrencia
'c=b-f(b)*(a-b)/(f(a)-f(b))
Cells.Clear
Cells(1, 1).Value = "Método Numérico de la Falsa Posición"
Cells(2, 2).Value = "Valor de X"
Cells(2, 3).Value = "Valor de Y"
Cells(2, 5).Value = " Xf "
Cells(2, 6).Value = " Yf "
Cells(2, 7).Value = "Iteraciones"
Xa = 1.35
Xb = 1.4
For j = 1 To 20
Ya = (Xa) ^ (3) + 2 * (Xa) ^ (2) + 10 * Xa - 20
Yb = (Xb) ^ (3) + 2 * (Xb) ^ (2) + 10 * Xb - 20
Xm = Xb - Yb * (Xa - Xb) / (Ya - Yb)
Ym = (Xm) ^ (3) + 2 * (Xm) ^ (2) + 10 * Xm - 20
If Ya * Ym < 0 Then Xb = Xm Else Xa = Xm
Error = Abs(Xa - Xb)
Cells(j + 3, 2).Value = Xm
Cells(j + 3, 3).Value = Ym
If Error <= 0.000001 Then Exit For
Next j
X = Xm
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 la Falsa Posición
Valor de X Valor de Y Xf Yf Iteraciones
1.368638564 -0.003576541 1.368808108 2.22045E-15 8
1.368806583 -3.21669E-05
1.368808094 -2.89284E-07
1.368808108 -2.60159E-09
1.368808108 -2.33955E-11
1.368808108 -2.08278E-13
1.368808108 -2.66454E-15
1.368808108 2.22045E-15