RichardsonExtrapolator

A simple code to perform 1D Richardson Extrapolation. This solves the extrapolation to $y(x_0)$ given a set of $x_i$ and $y(x_i)$ values.

There are two ways to use this code. First, if it is known that $(x_i-x_0)=\rho(x_{i+1}-x_0)\forall i$ (that is to say, the ratio of the points' progression to the goal point is known and constant for all $i$) then the known $1>\rho> 0$ value and a list of $y(x_i)$ values can be provided and the extrapolation performed. This is seen in example equal_space_example.txt and es_match_gen_example.txt, and is recommended if possible.

Alternatively, if the spacing between the points is not constant, then a list of $x_i$ and $y(x_i)$ pairs can be given (in order of $x_i$ furthest from $x_0$ to closest to $x_0$). Additionally, the desired $x_0$ value must be provided for this use-case. Then an iterative solve of the Richardson extrapolation will then be attempted for the given points. Note that the iterative solution of the extrapolation is not likely to succeed outside of the asymptotic region. This is seen in examples general_example.txt and gen_match_es_example.txt.

Note that the module src/richardson_module.f90 is portable and can be dropped into another program if desired.