added error benchmark

Author: xtalax

test/error_benchmarking.jl

@@ -0,0 +1,28 @@
+using DiffEqOperators, Plots
+
+n = 10000
+@show n
+x = range(0.0; length = n, stop = 2π)
+dx = x[2]-x[1]
+y = exp.(π*x)
+y_ = y[2:(end-1)]
+
+for dor in 1:4, aor in 2:6
+
+    D1 = CenteredDifference(dor,aor,dx,length(x))
+
+    #test result
+    @show dor
+    @show aor
+    #take derivatives
+    err_abs = abs.(D1*y .- (π^dor)*y_)
+    err_percent = 100*err_abs./abs.(((π^dor)*y_))
+    max_error = maximum(err_percent) # test operator with known derivative of exp(kx)
+    avg_error = sum(err_percent)/length(err_percent)
+
+    @show max_error
+    @show avg_error
+    plot(x[2:(end-1)], err_percent, title="Percentage Error, n=$n aor = $aor, dor = $dor")
+
+    #test result
+end