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 Numerical Methods Open Equations
Introduction
Open Equations
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When we are first introduced to equations, the equation format we are taught is closed equation format, that is y = f(x).

For example,
y = mx + cequation of a straight line
Q = UALmtddesign equation of heat exchanger

To write an equation in open equation format, the closed format equation is rearranged with all the terms on one side. The equation is then evaluated to find the residual. For example;

Closed Equation FormatOpen Equation Format
y = mx + cR = y - mx - c
Q = UALmtdR = Q - UALmtd

So why would we want to work with open equations?
  1. For linear equations, any term in the equation, (not just the left-hand term), can be found without the need rearrange the equation or solve it via iteration,
  2. If the model is over-specified the use of open equations provides a method to reconcile the data,
  3. Inter-related equations can be linked by simple connection equations can be used, rather than eliminating variables and equations