Order of accuracy

The order of accuracy, n, of a scheme is defined by the equation,

E(h) = h^n

where E is the error and h is the grid spacing. The error of a scheme should fall off with decreasing the grid spacing (i.e. the intercell distance), and how fast it falls off we say depends on the order of accuracy.

How to compute the error is the subject of the rest of this wiki page.

Computing the error for a scalar

This is the simplest type of error to compute. For a scalar function at one point (say the solution of an ODE at a given time), the error can be broken down as either absolute or relative.

The absolute error

If \hat{z} is your approximate solution, and z is the exact solution, then the absolute error is just given by E(h)=|\hat {z}-z|