##############ECHO OF PROBLEM################# ##############temp/arcsin_sqrtpostode.ode################# diff ( y , x , 1 ) = arcsin(sqrt(0.1 * x + 0.2)); ! /* BEGIN FIRST INPUT BLOCK */ Digits = 32; max_terms = 30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start = 0.1; x_end = 0.5 ; array_y_init[0 + 1] = exact_soln_y(x_start); glob_h = 0.05; glob_look_poles = true; glob_max_iter = 1000000; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_h = 0.00001 ; glob_look_poles = true; glob_max_iter = 100; glob_max_minutes = 1; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(10.0 * (0.1 * x + 0.2) * arcsin(sqrt ( 0.1 * x + 0.2)) + 5.0 * sqrt( 0.1 * x + 0.2) * sqrt( 0.8 - 0.1 * x) - 5.0 * arcsin(sqrt( 0.1 * x + 0.2))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.6560431130637943 y[1] (numeric) = 0.6560431130637943 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10001 y[1] (analytic) = 0.656047873408113 y[1] (numeric) = 0.6560478734081128 absolute error = 2.220446049250313e-16 relative error = 3.384579295585983e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10002 y[1] (analytic) = 0.6560526337647068 y[1] (numeric) = 0.6560526337647069 absolute error = 1.110223024625157e-16 relative error = 1.692277368439523e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10003 y[1] (analytic) = 0.656057394133577 y[1] (numeric) = 0.6560573941335768 absolute error = 2.220446049250313e-16 relative error = 3.384530178465175e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10004 y[1] (analytic) = 0.6560621545147218 y[1] (numeric) = 0.6560621545147223 absolute error = 4.440892098500626e-16 relative error = 6.769011240688742e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10005 y[1] (analytic) = 0.6560669149081433 y[1] (numeric) = 0.6560669149081434 absolute error = 1.110223024625157e-16 relative error = 1.69224053125831e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10006 y[1] (analytic) = 0.6560716753138401 y[1] (numeric) = 0.6560716753138401 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10007 y[1] (analytic) = 0.6560764357318122 y[1] (numeric) = 0.6560764357318124 absolute error = 2.220446049250313e-16 relative error = 3.384431947740273e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10008 y[1] (analytic) = 0.6560811961620604 y[1] (numeric) = 0.6560811961620603 absolute error = 1.110223024625157e-16 relative error = 1.692203695395832e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10009 y[1] (analytic) = 0.6560859566045836 y[1] (numeric) = 0.6560859566045837 absolute error = 1.110223024625157e-16 relative error = 1.692191417068049e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001 y[1] (analytic) = 0.6560907170593824 y[1] (numeric) = 0.6560907170593826 absolute error = 2.220446049250313e-16 relative error = 3.384358277773563e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10011 y[1] (analytic) = 0.6560954775264567 y[1] (numeric) = 0.656095477526457 absolute error = 3.33066907387547e-16 relative error = 5.076500582556084e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10012 y[1] (analytic) = 0.6561002380058067 y[1] (numeric) = 0.656100238005807 absolute error = 2.220446049250313e-16 relative error = 3.384309165927572e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10013 y[1] (analytic) = 0.6561049984974323 y[1] (numeric) = 0.6561049984974323 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10014 y[1] (analytic) = 0.6561097590013329 y[1] (numeric) = 0.6561097590013332 absolute error = 2.220446049250313e-16 relative error = 3.384260055253655e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001499999999999 y[1] (analytic) = 0.6561145195175095 y[1] (numeric) = 0.6561145195175094 absolute error = 1.110223024625157e-16 relative error = 1.692117750178105e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001599999999999 y[1] (analytic) = 0.6561192800459609 y[1] (numeric) = 0.6561192800459611 absolute error = 2.220446049250313e-16 relative error = 3.384210945751772e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001699999999999 y[1] (analytic) = 0.6561240405866879 y[1] (numeric) = 0.6561240405866881 absolute error = 1.110223024625157e-16 relative error = 1.692093195720166e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001799999999999 y[1] (analytic) = 0.65612880113969 y[1] (numeric) = 0.6561288011396904 absolute error = 4.440892098500626e-16 relative error = 6.768323674843773e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001899999999999 y[1] (analytic) = 0.6561335617049682 y[1] (numeric) = 0.6561335617049681 absolute error = 1.110223024625157e-16 relative error = 1.692068641848214e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001999999999999 y[1] (analytic) = 0.6561383222825206 y[1] (numeric) = 0.656138322282521 absolute error = 4.440892098500626e-16 relative error = 6.768225460527915e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002099999999999 y[1] (analytic) = 0.6561430828723491 y[1] (numeric) = 0.6561430828723492 absolute error = 1.110223024625157e-16 relative error = 1.692044088562231e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002199999999999 y[1] (analytic) = 0.6561478434744528 y[1] (numeric) = 0.6561478434744528 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002299999999999 y[1] (analytic) = 0.6561526040888316 y[1] (numeric) = 0.6561526040888316 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002399999999999 y[1] (analytic) = 0.6561573647154855 y[1] (numeric) = 0.6561573647154856 absolute error = 1.110223024625157e-16 relative error = 1.692007259731905e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002499999999999 y[1] (analytic) = 0.6561621253544143 y[1] (numeric) = 0.6561621253544148 absolute error = 4.440892098500626e-16 relative error = 6.767979934992373e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002599999999999 y[1] (analytic) = 0.6561668860056189 y[1] (numeric) = 0.6561668860056191 absolute error = 2.220446049250313e-16 relative error = 3.383965415821515e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002699999999999 y[1] (analytic) = 0.6561716466690983 y[1] (numeric) = 0.6561716466690987 absolute error = 3.33066907387547e-16 relative error = 5.075911296659694e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002799999999999 y[1] (analytic) = 0.6561764073448537 y[1] (numeric) = 0.6561764073448534 absolute error = 3.33066907387547e-16 relative error = 5.075874470026526e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002899999999999 y[1] (analytic) = 0.6561811680328835 y[1] (numeric) = 0.6561811680328832 absolute error = 3.33066907387547e-16 relative error = 5.075837643832775e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002999999999999 y[1] (analytic) = 0.6561859287331877 y[1] (numeric) = 0.656185928733188 absolute error = 3.33066907387547e-16 relative error = 5.075800818078432e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003099999999999 y[1] (analytic) = 0.6561906894457682 y[1] (numeric) = 0.656190689445768 absolute error = 2.220446049250313e-16 relative error = 3.383842661842316e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003199999999999 y[1] (analytic) = 0.6561954501706226 y[1] (numeric) = 0.656195450170623 absolute error = 3.33066907387547e-16 relative error = 5.075727167887914e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003299999999999 y[1] (analytic) = 0.6562002109077532 y[1] (numeric) = 0.656200210907753 absolute error = 1.110223024625157e-16 relative error = 1.691896781150576e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003399999999999 y[1] (analytic) = 0.6562049716571576 y[1] (numeric) = 0.6562049716571581 absolute error = 4.440892098500626e-16 relative error = 6.767538025939897e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003499999999999 y[1] (analytic) = 0.6562097324188381 y[1] (numeric) = 0.6562097324188381 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003599999999999 y[1] (analytic) = 0.6562144931927932 y[1] (numeric) = 0.656214493192793 absolute error = 2.220446049250313e-16 relative error = 3.38371991518626e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003699999999999 y[1] (analytic) = 0.656219253979023 y[1] (numeric) = 0.6562192539790229 absolute error = 1.110223024625157e-16 relative error = 1.691847683366886e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003799999999999 y[1] (analytic) = 0.6562240147775277 y[1] (numeric) = 0.6562240147775278 absolute error = 1.110223024625157e-16 relative error = 1.691835409287091e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003899999999999 y[1] (analytic) = 0.6562287755883073 y[1] (numeric) = 0.6562287755883075 absolute error = 2.220446049250313e-16 relative error = 3.383646270707482e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003999999999999 y[1] (analytic) = 0.6562335364113626 y[1] (numeric) = 0.6562335364113622 absolute error = 4.440892098500626e-16 relative error = 6.767243446267329e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004099999999998 y[1] (analytic) = 0.6562382972466916 y[1] (numeric) = 0.6562382972466917 absolute error = 1.110223024625157e-16 relative error = 1.691798587926367e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004199999999998 y[1] (analytic) = 0.6562430580942957 y[1] (numeric) = 0.6562430580942961 absolute error = 3.33066907387547e-16 relative error = 5.07535894329702e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004299999999998 y[1] (analytic) = 0.6562478189541748 y[1] (numeric) = 0.6562478189541752 absolute error = 3.33066907387547e-16 relative error = 5.075322123254244e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004399999999998 y[1] (analytic) = 0.656252579826329 y[1] (numeric) = 0.6562525798263291 absolute error = 1.110223024625157e-16 relative error = 1.691761767883589e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004499999999998 y[1] (analytic) = 0.6562573407107575 y[1] (numeric) = 0.6562573407107578 absolute error = 3.33066907387547e-16 relative error = 5.075248484486587e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004599999999998 y[1] (analytic) = 0.6562621016074612 y[1] (numeric) = 0.6562621016074612 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004699999999998 y[1] (analytic) = 0.6562668625164392 y[1] (numeric) = 0.6562668625164394 absolute error = 2.220446049250313e-16 relative error = 3.383449898317382e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004799999999998 y[1] (analytic) = 0.6562716234376922 y[1] (numeric) = 0.6562716234376923 absolute error = 1.110223024625157e-16 relative error = 1.691712676543241e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004899999999998 y[1] (analytic) = 0.6562763843712195 y[1] (numeric) = 0.6562763843712198 absolute error = 3.33066907387547e-16 relative error = 5.075101212222644e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004999999999998 y[1] (analytic) = 0.6562811453170219 y[1] (numeric) = 0.6562811453170221 absolute error = 2.220446049250313e-16 relative error = 3.38337626350321e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005099999999998 y[1] (analytic) = 0.656285906275099 y[1] (numeric) = 0.656285906275099 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005199999999998 y[1] (analytic) = 0.6562906672454504 y[1] (numeric) = 0.6562906672454505 absolute error = 1.110223024625157e-16 relative error = 1.691663587545634e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005299999999998 y[1] (analytic) = 0.6562954282280767 y[1] (numeric) = 0.6562954282280766 absolute error = 1.110223024625157e-16 relative error = 1.691651315662266e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005399999999998 y[1] (analytic) = 0.6563001892229772 y[1] (numeric) = 0.6563001892229773 absolute error = 1.110223024625157e-16 relative error = 1.691639043925309e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005499999999998 y[1] (analytic) = 0.6563049502301519 y[1] (numeric) = 0.6563049502301526 absolute error = 6.661338147750939e-16 relative error = 1.014976063400855e-13 % Correct digits = 14 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005599999999998 y[1] (analytic) = 0.6563097112496024 y[1] (numeric) = 0.6563097112496024 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005699999999998 y[1] (analytic) = 0.6563144722813264 y[1] (numeric) = 0.6563144722813267 absolute error = 2.220446049250313e-16 relative error = 3.383204459185731e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005799999999998 y[1] (analytic) = 0.6563192333253248 y[1] (numeric) = 0.6563192333253255 absolute error = 6.661338147750939e-16 relative error = 1.014953975064912e-13 % Correct digits = 14 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005899999999998 y[1] (analytic) = 0.6563239943815991 y[1] (numeric) = 0.6563239943815987 absolute error = 3.33066907387547e-16 relative error = 5.074733062309705e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005999999999998 y[1] (analytic) = 0.656328755450146 y[1] (numeric) = 0.6563287554501465 absolute error = 4.440892098500626e-16 relative error = 6.766261666312061e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006099999999998 y[1] (analytic) = 0.6563335165309684 y[1] (numeric) = 0.6563335165309686 absolute error = 2.220446049250313e-16 relative error = 3.383106291731703e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006199999999998 y[1] (analytic) = 0.6563382776240649 y[1] (numeric) = 0.6563382776240652 absolute error = 2.220446049250313e-16 relative error = 3.383081750600157e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006299999999998 y[1] (analytic) = 0.6563430387294358 y[1] (numeric) = 0.6563430387294361 absolute error = 3.33066907387547e-16 relative error = 5.074585814642076e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006399999999998 y[1] (analytic) = 0.6563477998470809 y[1] (numeric) = 0.6563477998470814 absolute error = 4.440892098500626e-16 relative error = 6.766065338430763e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006499999999998 y[1] (analytic) = 0.6563525609770007 y[1] (numeric) = 0.656352560977001 absolute error = 3.33066907387547e-16 relative error = 5.074512193443213e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006599999999997 y[1] (analytic) = 0.656357322119195 y[1] (numeric) = 0.656357322119195 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006699999999997 y[1] (analytic) = 0.6563620832736629 y[1] (numeric) = 0.6563620832736632 absolute error = 3.33066907387547e-16 relative error = 5.074438574000906e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006799999999997 y[1] (analytic) = 0.6563668444404056 y[1] (numeric) = 0.6563668444404057 absolute error = 1.110223024625157e-16 relative error = 1.69146725497948e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006899999999997 y[1] (analytic) = 0.656371605619422 y[1] (numeric) = 0.6563716056194225 absolute error = 5.551115123125783e-16 relative error = 8.457274927191831e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006999999999997 y[1] (analytic) = 0.6563763668107134 y[1] (numeric) = 0.6563763668107135 absolute error = 1.110223024625157e-16 relative error = 1.69144271604362e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007099999999997 y[1] (analytic) = 0.6563811280142786 y[1] (numeric) = 0.6563811280142787 absolute error = 1.110223024625157e-16 relative error = 1.691430446795242e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007199999999997 y[1] (analytic) = 0.6563858892301181 y[1] (numeric) = 0.6563858892301182 absolute error = 1.110223024625157e-16 relative error = 1.69141817769323e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007299999999997 y[1] (analytic) = 0.6563906504582318 y[1] (numeric) = 0.6563906504582318 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007399999999997 y[1] (analytic) = 0.6563954116986195 y[1] (numeric) = 0.6563954116986195 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007499999999997 y[1] (analytic) = 0.6564001729512809 y[1] (numeric) = 0.6564001729512814 absolute error = 4.440892098500626e-16 relative error = 6.765525485061437e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007599999999997 y[1] (analytic) = 0.6564049342162168 y[1] (numeric) = 0.6564049342162174 absolute error = 5.551115123125783e-16 relative error = 8.456845513743915e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007699999999997 y[1] (analytic) = 0.6564096954934271 y[1] (numeric) = 0.6564096954934274 absolute error = 3.33066907387547e-16 relative error = 5.074070503135676e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007799999999997 y[1] (analytic) = 0.6564144567829109 y[1] (numeric) = 0.6564144567829115 absolute error = 6.661338147750939e-16 relative error = 1.014806739692812e-13 % Correct digits = 14 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007899999999997 y[1] (analytic) = 0.6564192180846691 y[1] (numeric) = 0.6564192180846697 absolute error = 6.661338147750939e-16 relative error = 1.014799378846297e-13 % Correct digits = 14 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007999999999997 y[1] (analytic) = 0.6564239793987015 y[1] (numeric) = 0.6564239793987019 absolute error = 4.440892098500626e-16 relative error = 6.765280120583924e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008099999999997 y[1] (analytic) = 0.6564287407250078 y[1] (numeric) = 0.6564287407250081 absolute error = 3.33066907387547e-16 relative error = 5.073923287083433e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008199999999997 y[1] (analytic) = 0.6564335020635879 y[1] (numeric) = 0.6564335020635883 absolute error = 4.440892098500626e-16 relative error = 6.765181978890594e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008299999999997 y[1] (analytic) = 0.6564382634144417 y[1] (numeric) = 0.6564382634144424 absolute error = 7.771561172376096e-16 relative error = 1.183898259061344e-13 % Correct digits = 14 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008399999999997 y[1] (analytic) = 0.6564430247775703 y[1] (numeric) = 0.6564430247775705 absolute error = 2.220446049250313e-16 relative error = 3.382541919769337e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008499999999997 y[1] (analytic) = 0.6564477861529721 y[1] (numeric) = 0.6564477861529725 absolute error = 4.440892098500626e-16 relative error = 6.765034770740722e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008599999999997 y[1] (analytic) = 0.656452547540648 y[1] (numeric) = 0.6564525475406484 absolute error = 4.440892098500626e-16 relative error = 6.764985702528092e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008699999999997 y[1] (analytic) = 0.6564573089405975 y[1] (numeric) = 0.6564573089405982 absolute error = 6.661338147750939e-16 relative error = 1.014740495235117e-13 % Correct digits = 14 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008799999999997 y[1] (analytic) = 0.6564620703528214 y[1] (numeric) = 0.6564620703528218 absolute error = 3.33066907387547e-16 relative error = 5.073665675894072e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008899999999997 y[1] (analytic) = 0.6564668317773188 y[1] (numeric) = 0.6564668317773192 absolute error = 4.440892098500626e-16 relative error = 6.764838501402046e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008999999999997 y[1] (analytic) = 0.6564715932140901 y[1] (numeric) = 0.6564715932140904 absolute error = 3.33066907387547e-16 relative error = 5.073592076647959e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009099999999997 y[1] (analytic) = 0.6564763546631347 y[1] (numeric) = 0.6564763546631355 absolute error = 7.771561172376096e-16 relative error = 1.18382956479278e-13 % Correct digits = 14 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009199999999996 y[1] (analytic) = 0.6564811161244538 y[1] (numeric) = 0.6564811161244543 absolute error = 4.440892098500626e-16 relative error = 6.764691305543562e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009299999999996 y[1] (analytic) = 0.6564858775980458 y[1] (numeric) = 0.6564858775980468 absolute error = 9.992007221626409e-16 relative error = 1.522044504321284e-13 % Correct digits = 14 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009399999999996 y[1] (analytic) = 0.6564906390839123 y[1] (numeric) = 0.656490639083913 absolute error = 7.771561172376096e-16 relative error = 1.183803806132069e-13 % Correct digits = 14 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009499999999996 y[1] (analytic) = 0.6564954005820525 y[1] (numeric) = 0.6564954005820529 absolute error = 4.440892098500626e-16 relative error = 6.764544114952376e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009599999999996 y[1] (analytic) = 0.6565001620924659 y[1] (numeric) = 0.6565001620924665 absolute error = 6.661338147750939e-16 relative error = 1.014674257888867e-13 % Correct digits = 14 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009699999999996 y[1] (analytic) = 0.6565049236151532 y[1] (numeric) = 0.6565049236151538 absolute error = 5.551115123125783e-16 relative error = 8.455557488522168e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009799999999996 y[1] (analytic) = 0.6565096851501142 y[1] (numeric) = 0.6565096851501147 absolute error = 4.440892098500626e-16 relative error = 6.764396929628226e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009899999999996 y[1] (analytic) = 0.6565144466973492 y[1] (numeric) = 0.6565144466973492 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009999999999996 y[1] (analytic) = 0.6565192082568566 y[1] (numeric) = 0.6565192082568573 absolute error = 6.661338147750939e-16 relative error = 1.014644821350719e-13 % Correct digits = 14 h = 1e-05 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = arcsin(sqrt(0.1 * x + 0.2)); Iterations = 100 Total Elapsed Time = 18 Seconds Elapsed Time(since restart) = 18 Seconds Expected Time Remaining = 1 Hours 58 Minutes 30 Seconds Optimized Time Remaining = 1 Hours 51 Minutes 55 Seconds Time to Timeout = 42 Seconds Percent Done = 0.2525 %