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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

    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

    e.g. additional linear relation equation between similar quantities
    flow x = factor * flow y
  3. Concentration equation
    mass substance = mass good * concentration substance

    mass substance = volume good * concentration substance
    mass good = volume good * density good

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