test_deriv.c sine wave, to 4th order nx=17 
np is number of points used to compute derivative
np must be one larger than derivative and 11 too big for third
nx=17, xmin=0.000000, xmax=3.141593, hx=0.196350 
i=0, x=0.000000, u(x)=0.000000 
i=1, x=0.196350, u(x)=0.195090 
i=2, x=0.392699, u(x)=0.382683 
i=3, x=0.589049, u(x)=0.555570 
i=4, x=0.785398, u(x)=0.707107 
i=5, x=0.981748, u(x)=0.831470 
i=6, x=1.178097, u(x)=0.923880 
i=7, x=1.374447, u(x)=0.980785 
i=8, x=1.570796, u(x)=1.000000 
i=9, x=1.767146, u(x)=0.980785 
i=10, x=1.963495, u(x)=0.923880 
i=11, x=2.159845, u(x)=0.831470 
i=12, x=2.356194, u(x)=0.707107 
i=13, x=2.552544, u(x)=0.555570 
i=14, x=2.748894, u(x)=0.382683 
i=15, x=2.945243, u(x)=0.195090 
i=16, x=3.141593, u(x)=0.000000 

first,np=3, maxerr=1.267834e-02, avgerr=4.944549e-03 
first,np=4, maxerr=6.267826e-04, avgerr=4.317747e-04 
first,np=5, maxerr=2.797790e-04, avgerr=6.192074e-05 
first,np=6, maxerr=1.970916e-05, avgerr=5.622687e-06 
first,np=7, maxerr=7.054773e-06, avgerr=1.148028e-06 
first,np=8, maxerr=7.975510e-07, avgerr=1.337510e-07 
first,np=9, maxerr=1.842452e-07, avgerr=2.621058e-08 
first,np=10, maxerr=3.075718e-08, avgerr=4.336972e-09 
first,np=11, maxerr=4.735354e-09, avgerr=6.344319e-10 


second,np=4, maxerr=7.473156e-03, avgerr=2.795538e-03 
second,np=5, maxerr=5.964373e-03, avgerr=7.812157e-04 
second,np=6, maxerr=4.455191e-04, avgerr=6.701106e-05 
second,np=7, maxerr=1.769523e-04, avgerr=2.300366e-05 
second,np=8, maxerr=2.080018e-05, avgerr=2.737418e-06 
second,np=9, maxerr=5.129668e-06, avgerr=6.566615e-07 
second,np=10, maxerr=8.805267e-07, avgerr=1.124220e-07 
second,np=11, maxerr=1.422131e-07, avgerr=1.795603e-08 


third,np=5, maxerr=6.432577e-02, avgerr=1.267435e-02 
third,np=6, maxerr=5.300455e-03, avgerr=1.224085e-03 
third,np=7, maxerr=2.509396e-03, avgerr=3.403011e-04 
third,np=8, maxerr=3.129189e-04, avgerr=4.264575e-05 
third,np=9, maxerr=8.520029e-05, avgerr=1.038596e-05 
third,np=10, maxerr=1.521875e-05, avgerr=1.859186e-06 
third,np=11, maxerr=2.112083e+05, avgerr=2.484803e+04 


fourth,np=5, maxerr=3.802316e-01, avgerr=7.019394e-02 
fourth,np=6, maxerr=3.667335e-02, avgerr=9.566014e-03 
fourth,np=7, maxerr=2.343146e-02, avgerr=3.414689e-03 
fourth,np=8, maxerr=3.179920e-03, avgerr=4.648849e-04 
fourth,np=9, maxerr=1.000663e-03, avgerr=1.320278e-04 
fourth,np=10, maxerr=1.886047e-04, avgerr=2.450480e-05 


nx=17, xmin=0.000000, xmax=6.283185, hx=0.392699 
i=0, x=0.000000, u(x)=0.000000 
i=1, x=0.392699, u(x)=0.382683 
i=2, x=0.785398, u(x)=0.707107 
i=3, x=1.178097, u(x)=0.923880 
i=4, x=1.570796, u(x)=1.000000 
i=5, x=1.963495, u(x)=0.923880 
i=6, x=2.356194, u(x)=0.707107 
i=7, x=2.748894, u(x)=0.382683 
i=8, x=3.141593, u(x)=0.000000 
i=9, x=3.534292, u(x)=-0.382683 
i=10, x=3.926991, u(x)=-0.707107 
i=11, x=4.319690, u(x)=-0.923880 
i=12, x=4.712389, u(x)=-1.000000 
i=13, x=5.105088, u(x)=-0.923880 
i=14, x=5.497787, u(x)=-0.707107 
i=15, x=5.890486, u(x)=-0.382683 
i=16, x=6.283185, u(x)=-0.000000 

first,np=3, maxerr=4.867440e-02, avgerr=1.931089e-02 
first,np=4, maxerr=6.750430e-03, avgerr=3.833526e-03 
first,np=5, maxerr=3.683021e-03, avgerr=8.663717e-04 
first,np=6, maxerr=1.124213e-03, avgerr=2.455703e-04 
first,np=7, maxerr=2.593482e-04, avgerr=4.556399e-05 
first,np=8, maxerr=1.616385e-04, avgerr=2.507665e-05 
first,np=9, maxerr=9.353536e-06, avgerr=1.483898e-06 
first,np=10, maxerr=2.092331e-05, avgerr=2.893924e-06 
first,np=11, maxerr=1.682972e-06, avgerr=2.389619e-07 


second,np=4, maxerr=5.751522e-02, avgerr=1.432831e-02 
second,np=5, maxerr=3.990286e-02, avgerr=5.303164e-03 
second,np=6, maxerr=1.275306e-02, avgerr=1.789661e-03 
second,np=7, maxerr=3.336266e-03, avgerr=4.341435e-04 
second,np=8, maxerr=2.117069e-03, avgerr=2.759096e-04 
second,np=9, maxerr=1.409345e-04, avgerr=1.784220e-05 
second,np=10, maxerr=3.010826e-04, avgerr=3.835432e-05 
second,np=11, maxerr=2.387130e-05, avgerr=3.048014e-06 


third,np=5, maxerr=2.215128e-01, avgerr=4.533195e-02 
third,np=6, maxerr=7.632635e-02, avgerr=1.388815e-02 
third,np=7, maxerr=2.460621e-02, avgerr=3.482202e-03 
third,np=8, maxerr=1.603143e-02, avgerr=2.073522e-03 
third,np=9, maxerr=1.302928e-03, avgerr=1.700582e-04 
third,np=10, maxerr=2.621713e-03, avgerr=3.175053e-04 
third,np=11, maxerr=2.791983e+04, avgerr=3.284686e+03 


fourth,np=5, maxerr=6.891414e-01, avgerr=1.310124e-01 
fourth,np=6, maxerr=2.666109e-01, avgerr=5.644822e-02 
fourth,np=7, maxerr=1.217788e-01, avgerr=1.745522e-02 
fourth,np=8, maxerr=8.224908e-02, avgerr=1.169738e-02 
fourth,np=9, maxerr=8.763509e-03, avgerr=1.106353e-03 
fourth,np=10, maxerr=1.641503e-02, avgerr=2.119476e-03 


test_deriv.c finished