Run-time error 5?

Question

I am trying to define a derivative function for solving a system of differential equations, however when I run the actual macro that calls up this sub routine, i keep getting Run-time error 5: Invalid procedure call or argument. This error occurs in the If statement when x is not greater than 1 and Qv is to be calculated using the equation provided. While stepping into to debug, there are values for all of the variables, but it gives me the error and I have no idea why. Can someone help please?

Sub Derivs(x As Double, y() As Double, dydx() As Double)

Const g As Double = 32.1740485564
Const Hr As Double = 100
Const h0 As Double = 80
Const fm As Double = 0.024
Const L As Double = 1500
Const dp As Double = 2
Const tc As Double = 5
Const k As Double = 25.7
Const Di As Double = 5

Dim u0 As Double
Dim Qv As Double
Dim Qv0 As Double
Dim hstar As Double

u0 = ((g * h0 / ((1 / 2) * fm * (L / dp))) * ((Hr / h0) - 1)) ^ (1 / 2)

Qv0 = (u0 * 3.14 * Di ^ 2) / 4

hstar = h0 - (Qv0 / k) ^ 2

If x >= 1 Then
    Qv = 0
Else
    Qv = k * (h0 ^ 0.5) * (1 - x) * (y(1) - hstar / h0) ^ 0.5
End If

dydx(0) = ((tc * g * h0) / (L * u0)) * (((Hr / h0) - y(1)) - ((Hr / h0) - 1) * y(0) * Abs(y(0)))

dydx(1) = ((dp / Di) ^ 2) * (u0 * tc / h0) * y(0) - ((4 * Qv * tc) / (3.14 * h0 * Di ^ 2))

End Sub

Well the macro that calls this sub routine is:

Sub RungeKutta()

Dim y(1) As Double
Dim dydx(1) As Double
Dim yout(1) As Double
Dim yerr(1) As Double
Dim x As Double
Dim hdid As Double
Dim yscal(1) As Double
Dim hnext As Double
Dim ystart(1) As Double
Dim NOk As Integer
Dim NBad As Integer
Dim h As Double

Const n As Integer = 2
Dim htry As Double
Const eps As Double = 0.00000001
Dim x1 As Double
Dim x2 As Double
Const nvar As Integer = 2
Dim h1 As Double
Const hmin As Double = 0.001

h = 0.001
x1 = 0
x2 = 10
h1 = 0.01
x = x1
h = Sgn(x2 - x1) * Abs(h1)
NOk = 0
NBad = 0
kount = -1

x = 0

y(0) = 1#
y(1) = 1#

Call Derivs(x, y(), dydx())

Call odeint(ystart(), nvar, x1, x2, eps, h1, hmin, NOk, NBad)

' I have a bunch of coding to input the calculations into a spreadsheet that I am omitting

End Sub

The main program in the macro is:

Sub odeint(ystart() As Double, nvar As Integer, x1 As Double, x2 As Double, eps As Double, h1 As Double, hmin As Double, NOk As Integer, NBad As Integer)

Const MaxStp As Double = 10000
Const Tiny As Double = 10 ^ (-30)

Dim y() As Double
Dim yscal() As Double
Dim dydx() As Double
Dim x As Double
Dim h As Double
Dim hdid As Double
Dim hnext As Double
Const n As Integer = 2

NM1 = n - 1

nvar = 2

ReDim y(NM1)
ReDim dydx(NM1)
ReDim yscal(NM1)


x = x1
h = Sgn(x2 - x1) * Abs(h1)
NOk = 0
NBad = 0
kount = -1

kmax = 500

ReDim xp(kmax)
ReDim yp(NM1, kmax)

dxsav = (x2 - x1) / kmax


For I = 0 To nvar - 1
    y(I) = ystart(I)

Next I

If kmax > 0 Then xsav = x - 2 * dxsav
    For nstp = 1 To MaxStp
        Call Derivs(x, y(), dydx())

        For I = 0 To nvar - 1
            yscal(I) = Abs(y(I)) + Abs(h * dydx(I)) + Tiny
        Next I

        If kmax > 0 Then

            If Abs(x - xsav) > Abs(dxsav) Then

                If kount < kmax - 1 Then
                    kount = kount + 1
                    xp(kount) = x

                    For I = 0 To nvar - 1
                        yp(I, kount) = y(I)
                    Next I

                    xsav = x
                End If
            End If
        End If
        If (x + h - x2) * (x + h - x1) > 0 Then h = x2 - x
            Call rkqs(y(), dydx(), nvar, x, h, eps, yscal(), hdid, hnext)
            If hdid = h Then
                NOk = NOk + 1
            Else
                NBad = NBad + 1
            End If

            If (x - x2) * (x2 - x1) >= 0 Then
                For I = 0 To nvar - 1
                    ystart(I) = y(I)
                Next I

                If Not kmax = 0 Then
                    kount = kount + 1
                    xp(kount) = x

                    For I = 0 To nvar - 1
                        yp(I, kount) = y(I)
                    Next I
                End If
                Exit Sub
            End If

            If Abs(hnext) < hmin Then MsgBox "Stepsize smaller than minimum in odeint!", vbExclamation

            h = hnext
    Next nstp

MsgBox "Too many steps in odeint", vbExclamation

End Sub

Which calls this sub routine:

Sub rkqs(y() As Double, dydx() As Double, n As Integer, x As Double, htry As Double, eps As Double, yscal() As Double, hdid As Double, hnext As Double)

NM1 = n - 1

Dim ytemp() As Double
Dim yerr() As Double
Dim h As Double
Const Tiny As Double = 10 ^ (-30)

ReDim ytemp(NM1)
ReDim yerr(NM1)

Const Safety As Double = 0.9
Const PGrow As Double = -0.2
Const PShrink As Double = -0.25
Const ErrCon As Double = (5# / Safety) ^ (1# / PGrow)

h = htry
Do
    Call rkck(y(), dydx(), n, x, h, ytemp(), yerr())

    ErrMax = 0

    For I = 0 To NM1
            yscal(I) = Abs(y(I)) + Abs(h * dydx(I)) + Tiny
        Next I

    For I = 0 To n - 1
        If Abs(yerr(I) / yscal(I)) > ErrMax Then ErrMax = Abs(yerr(I) / yscal(I))
    Next I

    ErrMax = ErrMax / eps

    If ErrMax > 1 Then
        dummy = h
        h = Safety * h * (ErrMax ^ PShrink)

        If h < 0.1 * dummy Then
            h = 0.1 * dummy
        End If

        xNew = x + h

        If xNew = x Then MsgBox "Stepsize underflow in rkqsl", vbExclamation
        ContLoop = True

    Else
        If ErrMax > ErrCon Then
            hnext = Safety * h * (ErrMax ^ PGrow)
        Else
            hnext = 5 * h
        End If

        hdid = h

        x = x + h

        For I = 0 To n - 1
            y(I) = ytemp(I)
        Next I

        ContLoop = False
    End If

Loop While ContLoop

End Sub

which then calls this subroutine:

Sub rkck(y() As Double, dydx() As Double, n As Integer, x As Double, h As Double, yout() As Double, yerr() As Double)

Dim NM1 As Integer
Dim I As Integer
Dim ak2() As Double
Dim ak3() As Double
Dim ak4() As Double
Dim ak5() As Double
Dim ak6() As Double
Dim ytemp() As Double

NM1 = n - 1

ReDim ak2(NM1)
ReDim ak3(NM1)
ReDim ak4(NM1)
ReDim ak5(NM1)
ReDim ak6(NM1)
ReDim ytemp(NM1)

Const A2 As Double = 1# / 5#
Const A3 As Double = 3# / 10#
Const A4 As Double = 3# / 5#
Const A5 As Double = 1#
Const A6 As Double = 7# / 8#

Const B21 As Double = 1# / 5#
Const B31 As Double = 3# / 40#
Const B32 As Double = 9# / 40#
Const B41 As Double = 3# / 10#
Const B42 As Double = -9# / 10#
Const B43 As Double = 6# / 5#
Const B51 As Double = -11# / 54#
Const B52 As Double = 5# / 2#
Const B53 As Double = -70# / 27#
Const B54 As Double = 35# / 27#
Const B61 As Double = 1631# / 55296#
Const B62 As Double = 175# / 512#
Const B63 As Double = 575# / 13824#
Const B64 As Double = 44275# / 110592#
Const B65 As Double = 253# / 4096#

Const C1 As Double = 37# / 378#
Const C3 As Double = 250# / 621#
Const C4 As Double = 125# / 594#
Const C6 As Double = 512# / 1771#

Const DC1 As Double = C1 - 2825# / 27648#
Const DC3 As Double = C3 - 18575# / 48384#
Const DC4 As Double = C4 - 13525# / 55296#
Const DC5 As Double = -277# / 14336#
Const DC6 As Double = C6 - 1# / 4#

'First Step
For I = 0 To n - 1
    ytemp(I) = y(I) + B21 * h * dydx(I)
Next I

'Second Step
Call Derivs(x + A2 * h, ytemp(), ak2())

For I = 0 To n - 1
    ytemp(I) = y(I) + h * (B31 * dydx(I) + B32 * ak2(I))
Next I

'Third Step
Call Derivs(x + A3 * h, ytemp(), ak3())

For I = 0 To n - 1
    ytemp(I) = y(I) + h * (B41 * dydx(I) + B42 * ak2(I) + B43 * ak3(I))
Next I

'Fourth Step
Call Derivs(x + A4 * h, ytemp(), ak4())

For I = 0 To n - 1
    ytemp(I) = y(I) + h * (B51 * dydx(I) + B52 * ak2(I) + B53 * ak3(I) + B54 * ak4(I))
Next I

'Fifth Step
Call Derivs(x + A5 * h, ytemp(), ak5())

For I = 0 To n - 1
    ytemp(I) = y(I) + h * (B61 * dydx(I) + B62 * ak2(I) + B63 * ak3(I) + B64 * ak4(I) + B65 * ak5(I))
Next I

'Sixth Step
Call Derivs(x + A6 * h, ytemp(), ak6())

For I = 0 To n - 1
    yout(I) = y(I) + h * (C1 * dydx(I) + C3 * k3(I) + C4 * ak4(I) + C6 * ak6(I))
Next I

For I = 0 To n - 1
    yerr(I) = h * (DC1 * dydx(I) + DC3 * ak3(I) + DC4 * ak4(I) + DC5 * ak5(I) + DC6 * ak6(I))
Next I

End Sub

It's the Runge Kutta method.

So I debugged each of the three programs separately starting with RKCK, then going into RKQS and then to ODEINT by essentially writing test macros for each that included all the parameters, outputted the calculated values accosted with each program in a message box, and called the following example set of equations:

Sub Derivs1(x As Double, y() As Double, dydx() As Double)


dydx(0) = -2 * x * y(0)

dydx(1) = -3 * y(1) * x ^ 2

End Sub

Each program worked perfectly for this example so I decided to test each test macro with the actual problem statement equations. RKCK worked fine, so did RKQS. Then when I got to the ODEINT, the error message popped up.

Answer 1

Run time error 5 is an "Invalid Procedure call" error.

I can't see how that line could produce an error as long the y array has a value at index 1.

You need to give an example of calling this function similar to the following which runs without any error.

Sub test()
Dim dydx(0 To 1) As Double
Dim y(0 To 1) As Double
dydx(0) = 1
dydx(1) = 2
y(0) = 1
y(1) = 2
Derivs 0.5, y, dydx

End Sub

I've run your edited code and when the error occurs in

Qv = k * (h0 ^ 0.5) * (1 - x) * (y(1) - hstar / h0) ^ 0.5

your variable values are:

y(1) = 0
hstar = 38.3
h0 = 80

This means:

(y(1) - hstar / h0) = -0.478857734838603

As Jean-François Corbett mentioned, the square root of a -ve number isn't supported by vba and results in the run-time error 5.

Answer 2

You're probably taking the square root of a negative.

x ^ 0.5 will give you an "Invalid procedure call or argument" error when x is negative.

Try stepping through your code in debug mode to confirm this.