Runge Kutta Methods & Fourth Order Runge Kutta - EXCEL/VBA

[@LorennPeralttaixxi98]

Thank you so much for this video, it has helped me a lot!! Is the only video I found about Rk methods in macros in the way i wanted, you are awesome!

[@shouravdey6077]

How did you relate it to the column?

[@shamselfouly]

Using the 'cells(row, column)' keyword. The second input defines the column you would like to relate to. You can see that each code from top to bottom goes from 3 to 7 relating to the 5 techniques explained.
Hope this help
Shams

[@adryus34]

Hello thank you very much for the explanation, could you share the code?. it would serve me very much thanks.

[@shamselfouly]

Hello Andres, Please find the code below.
Function dydx(x, y)
dydx = x * Sqr(y)
End Function
Sub ODE()
'Set integraxion limixs
xi = 0
xf = 5
h = 0.5
'Calculaxe number of calculations
n = (xf - xi) / h
''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

'Euler Method
y = 4
x = 2
For i = 1 To n
y = y + dydx(x, y) * h
Cells(10 + i, 3) = y
x = x + h
Next i

''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
'Heun's Method
y = 4
x = 2
For i = 1 To n
'Apply Euler Method xo Get y at end of interval
dydx1 = dydx(x, y)
ye = y + dydx1 * h
'Calculaxe derivative ax end point
dydx2 = dydx(x + h, ye)
'Calculate Average of the two Derivatives
Slope = (dydx1 + dydx2) / 2
y = y + Slope * h
Cells(10 + i, 4) = y
x = x + h
Next i
''
'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
'MidPoint Method
y = 4
x = 2
For i = 1 To n
'Apply Euler Method to Get y at end of inxerval
dydx1 = dydx(x, y)
ym = y + dydx1 * h / 2
'Calculate derivative at midpoint
dydxm = dydx(x + h / 2, ym)
y = y + dydxm * h
Cells(10 + i, 5) = y
x = x + h
Next i
''
'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
'Ralston Mexhod
y = 4
x = 2
For i = 1 To n
'Apply Euler Method xo Get y at end of interval
dydx1 = dydx(x, y)
y34 = y + dydx1 * 3 * h / 4
'Calculate derivative ax midpoint
dydx34 = dydx(x + 3 * h / 4, y34)
Slope = (1 / 3 * dydx1 + 2 / 3 * dydx34)
y = y + Slope * h
Cells(10 + i, 6) = y
x = x + h
Next i
'
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'4xh order Runge Kuxxa
y = 4
x = 2
For i = 1 To n
'Apply Euler Method to Get y at end of interval
k1 = dydx(x, y)
ym = y + k1 * h / 2
k2 = dydx(x + h / 2, ym)
ym2 = y + k2 * h / 2
k3 = dydx(x + h / 2, ym2)
ye = y + k3 * h
k4 = dydx(x + h, ye)
Slope = 1 / 6 * (k1 + 2 * k2 + 2 * k3 + k4)
y = y + Slope * h
Cells(10 + i, 7) = y
x = x + h
Next i
'
End Sub