For example, in Euler's method (see discretization) the global error, or global discretization error, is the error in the discrete solution to the problem, specifically yn – y(xn)
The local discretization error is the amount by which the continuous solution fails to satisfy the discrete formula: (1/h)(y(xn+1) – y(xn)) – f(xn,y(xn))
Speaking generally, estimates of local errors are used in choosing the grid spacing h hence providing a means of indirectly controlling the global error.
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