Convergence Speed For Discretization Methods
A similar situation exists for discretization methods. The important parameter here for the convergence speed is not the iteration number k but it depends on the number of grid points and grid spacing. In this case, the number of grid points in a discretization process is inversely proportional to the grid spacing here it denoted as n.
In this case, a sequence is said to converge to L with order p if there exists a constant C such that
This is written as |xn - L| = O(n-p) using the big O notation.
This is the relevant definition when discussing methods for numerical quadrature or the solution of ordinary differential equations.
Read more about this topic: Rate Of Convergence
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