**The iterative method** uses an under-relaxation f=
actor of w for the first iteration and subsequent iterations until the conv=
ergence criteria is satisfied.

The notation used in the iterative process is listed in the Variable Not=
ation table in the =
Partial Differential Equations section. The first iteration estimate of=
Y^{n+1/2} and Q^{n+1/2} are Y^{n and Qn, respectively. Typical r=
anges of w are 0.5 to 0.75. The new estimate of Qn+1 at each iteration is:<=
/p>
}

**Equation 22: =
**Qn+1 =3D (1-w)=C2=B7Qn+1/2 + w=C2=B7Qn+1

and the estimated new junc= tion depth at each iteration is:

**Equation 23: **Yn+1 =3D (1-w)=C2=B7Yn=
+1/2 + =C2=B7wYn+1

The new time step solution=
is deemed solved when all the estimated conduit flows and junction depths =
satisfy their convergence criterion (parameters Maximum Head Change (

**Equation 24: |Q _{n+1} - Q_{n+1/2}|/Q_{n+1} < SURTO=
L **

**Equation 25: **|A_{n+1} - A_{n+1/2|/An+1 <SURTOL }

**Equation 26: =
**|Y_{n+1} - Y_{n+1/2}|/Y_{n+1<=
/sub> < SURTOL&nb=
sp;}

**Equation 27: =
**|V_{n+1} - V_{n}|/V_{n+1 < SURTOL <=
/p>
}

**Qref**, the=
reference full conduit flow, is defined by the user in the Job Control dia=
log and allows a more realistic convergence criteria for large conduits.

The convergence of the con= duit cross section area as well as the conduit flow is tested to prevent th= e decoupling of A and Q, since the estimate of A is based on the last itera= tion value of the connecting node depths. Please note that the magnitude of= Aref is assumed equal to the magnitude of Qref and is not entered in a dia= log.

An additional bound on the=
iterated values of junction head and conduit flows is used in EXTRAN versi=
on 5. The change in H is restricted __<__=
1 percent in any one iteration, and the change in Q is restricted __<__10 percent in any one iteration.

This depth computation is = based on the current net inflows to each node and the average nodal surface= areas computed for the last time step and the current iteration. The new w= ater surface elevation in the junction must be within the limits defined by= the ground and invert elevations. The new junction elevation is calculated= by weighting the last and current iteration using an under-relaxation para= meter (w). The change in depth is additionally constrained to be less than = 1 percent in any one iteration. Larger changes are adjusted to 105 or 95 pe= rcent of the calculated depth.

The continuity equation at= the nodes is tested for convergence using the global parameter, SURJUN (Ma= ximum Flow Change), defined in the JOB CONTROL dialog. The nodal convergenc= e check constrains the error in the nodal continuity equation divided by th= e crown depth (Node ground elevation minus invert elevation) to be less tha= n the value of SURJUN. Typical values of SURJUN are 0.005 and 0.001 (ft or = m).