Merge pull request #143 from xtalax/fix-#136

Fix #136 - add error benchmarking

Author: ChrisRackauckas

src/derivative_operators/derivative_operator.jl

@@ -20,7 +20,7 @@ struct CenteredDifference{N} end
 function CenteredDifference{N}(derivative_order::Int,
                             approximation_order::Int, dx::T,
                             len::Int, coeff_func=nothing) where {T<:Real,N}
-
+    @assert approximation_order>1 "approximation_order must be greater than 1."
     stencil_length          = derivative_order + approximation_order - 1 + (derivative_order+approximation_order)%2
     boundary_stencil_length = derivative_order + approximation_order
     dummy_x                 = -div(stencil_length,2) : div(stencil_length,2)

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