Option Explicit

Private Sub CommandButton1_Click()
    Dim x As Double, y As Double, z As Double
    Dim xd As Double, yd As Double
    
    Dim kx(13) As Double
    Dim ky(13) As Double
    Dim a(13) As Double
    Dim b(13, 13) As Double
    Dim c(13) As Double
        
    Dim t As Double, dt As Double
    Dim i As Long, j As Integer, k As Integer, jj As Integer
    Dim pi As Double
    Application.ScreenUpdating = False
    
    
    a(1) = 0#
    a(2) = 2# / 27#
    a(3) = 1# / 9#
    a(4) = 1# / 6#
    a(5) = 5# / 12#
    a(6) = 0.5
    a(7) = 5# / 6#
    a(8) = 1# / 6#
    a(9) = 2# / 3#
    a(10) = 1# / 3#
    a(11) = 1#
    a(12) = 0#
    a(13) = 1
    For j = 1 To 13
        For k = 1 To 13
            b(j, k) = 0
        Next k
        kx(j) = 0#
        ky(j) = 0#
    Next j
    
    b(2, 1) = 2# / 27#
    
    b(3, 1) = 1# / 36
    b(3, 2) = 1# / 12#
    
    b(4, 1) = 1# / 24#
    b(4, 3) = 1# / 8#
    
    b(5, 1) = 5# / 12#
    b(5, 3) = -25# / 16#
    b(5, 4) = 25# / 16#
    
    b(6, 1) = 1# / 20#
    b(6, 4) = 1# / 4#
    b(6, 5) = 1# / 5#
    
    b(7, 1) = -25# / 108#
    b(7, 4) = 125# / 108#
    b(7, 5) = -65# / 27#
    b(7, 6) = 125# / 54#
    
    b(8, 1) = 31# / 300#
    b(8, 5) = 61# / 225#
    b(8, 6) = -2# / 9#
    b(8, 7) = 13# / 900#
    
    b(9, 1) = 2#
    b(9, 4) = -53# / 6#
    b(9, 5) = 704# / 45#
    b(9, 6) = -107# / 9#
    b(9, 7) = 67# / 90#
    b(9, 8) = 3#
    
    b(10, 1) = -91# / 108#
    b(10, 4) = 23# / 108#
    b(10, 5) = -976# / 135#
    b(10, 6) = 311# / 54#
    b(10, 7) = -19# / 60#
    b(10, 8) = 17# / 6#
    b(10, 9) = -1# / 12#
    
    b(11, 1) = 2383# / 4100#
    b(11, 4) = -341# / 164#
    b(11, 5) = 4496# / 1025#
    b(11, 6) = -301# / 82#
    b(11, 7) = 2133# / 4100#
    b(11, 8) = 45# / 82#
    b(11, 9) = 45# / 164#
    b(11, 10) = 18# / 41#
    
    b(12, 1) = 3# / 205#
    b(12, 6) = -6# / 41#
    b(12, 7) = -3# / 205#
    b(12, 8) = -3# / 41#
    b(12, 9) = 3# / 41#
    b(12, 10) = 6# / 41#
    
    b(13, 1) = -1777# / 4100#
    b(13, 4) = -341# / 164#
    b(13, 5) = 4496# / 1025#
    b(13, 6) = -289# / 82#
    b(13, 7) = 2193# / 4100#
    b(13, 8) = 51# / 82#
    b(13, 9) = 33# / 164#
    b(13, 10) = 12# / 41#
    b(13, 12) = 1#
    
    c(6) = 34# / 105#
    c(7) = 9# / 35#
    c(8) = 9# / 35#
    c(9) = 9# / 280#
    c(10) = 9# / 280#
    c(12) = 41# / 840#
    c(13) = 41# / 840#
    
    pi = 3.14159265358979
    x = 0#
    
    y = 0#
    t = 0
    dt = 2# * pi / 1000#
    jj = 1
    
    For i = 0 To 30000000
        If i Mod 1000 = 0 Then
            Worksheets("Sheet1").Cells(jj, 3) = t
            Worksheets("Sheet1").Cells(jj, 4) = x
            Worksheets("Sheet1").Cells(jj, 5) = y
            jj = jj + 1
        End If
        
        
        kx(1) = f1(t + dt, x, y) * dt
        ky(1) = f2(t + dt, x, y) * dt
        
        For j = 2 To 13
            xd = x
            yd = y
            For k = 1 To j - 1
                xd = xd + b(j, k) * kx(k)
                yd = yd + b(j, k) * ky(k)
            Next k
            kx(j) = f1(t + a(j) * dt, xd, yd) * dt
            ky(j) = f2(t + a(j) * dt, xd, yd) * dt
        Next j
        
        
        For j = 1 To 13
            x = x + c(j) * kx(j)
            y = y + c(j) * ky(j)
        Next j

        t = t + dt
        
    Next i
    Application.ScreenUpdating = True
End Sub

Function f1(t As Double, x As Double, y As Double) As Double
    f1 = y
End Function

Function f2(t As Double, x As Double, y As Double) As Double
    f2 = -0.05 * y - 1# * x * x * x + 7.5 * Cos(1# * t)
End Function