lambda =10;exact = x ->sinh(lambda*x)/sinh(lambda) -1;p = x ->0;q = x ->-lambda^2;r = x -> lambda^2;
n =5*[round(Int,10^d) for d in0:.25:3];err =zeros(size(n));for (k,n) inenumerate(n) x,u = FNC.bvplin(p,q,r,[0,1],-1,0,n) err[k] =norm(exact.(x)-u,Inf)enddata = (n=n[1:4:end],err=err[1:4:end]);pretty_table(data,["n","max-norm error"])
plot(n,err,m=:o,label="observed", xaxis=(:log10,L"n"), yaxis=(:log10,"max-norm error"), title="Convergence for a linear BVP");plot!(n,0.25*n.^(-2),l=(:dash,:gray),label="2nd order")