A linear equation is one that, when graphed, forms a straight line. For example,
y = 2x. The graph of this is as follows:
Non-linearity describes an equation that forms a graph that is not a straight line. An example of this type of equation is as follows: y = x2
Linear equations are much easier to work with than non-linear equations. With a linear equation, a formula can be found to quickly solve the equation for the nth iteration. In other words, they are predictable and consequently, the equation doesn’t have to be run to find a certain result. Example: to calculate xnext = x + 3 to the nth iteration, the formula would be as follows: x = n * 3.
However, the majority of non-linear equations are non-predictable. Example:
znext = zn2 + 2 – 3I has general solution
in terms of n.
