System of Equations

In order to describe the model in a mathematical way 3 types of equations are used:

1. Mass conservation
   e.g. balance equation
   sum of inputs = sum of outputs + change in stock
   
   
   
   or
   e.g. stock equation
   stock _i = stock _{i -1}+ change in stock _i-1
   with i…period
   
   i.e. the amount of stock at the beginning of a period can be calculated from the amount of stock in the previous period plus the change in stock during this previous period.
2. Linear relations
   e.g. transfer coefficient equation
   output 1 = TC1 * Sum of inputs
   output 2 = TC2 * Sum of inputs
   with TC1 + TC2 = 1
   
   
   
   or
   e.g. additional linear relation equation between similar quantities
   flow x = factor * flow y

3. Concentration equation
   mass _substance = mass _good * concentration _{substance in good}
   
   
   or
   mass _substance = volume _good * concentration _{substance in good}
   mass _good = volume _good * density _good