##############ECHO OF PROBLEM################# ##############temp/arctan_sqrtpostode.ode################# diff ( y , x , 1 ) = arctan(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) * arctan(sqrt ( 0.1 * x + 0.2)) - 10.0 * sqrt( 0.1 * x + 0.2) + 10.0 * arctan(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) = 0.6167902654763967 y[1] (numeric) = 0.6167902654763967 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) = 0.616794562477567 y[1] (numeric) = 0.6167945624775668 absolute error = 2.220446049250313e-16 relative error = 3.599976692938293e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10002 y[1] (analytic) = 0.6167988594877545 y[1] (numeric) = 0.6167988594877541 absolute error = 3.33066907387547e-16 relative error = 5.39992741984244e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10003 y[1] (analytic) = 0.6168031565069589 y[1] (numeric) = 0.6168031565069587 absolute error = 2.220446049250313e-16 relative error = 3.599926533815106e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10004 y[1] (analytic) = 0.6168074535351806 y[1] (numeric) = 0.6168074535351805 absolute error = 1.110223024625157e-16 relative error = 1.799950727349363e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10005 y[1] (analytic) = 0.6168117505724192 y[1] (numeric) = 0.6168117505724194 absolute error = 2.220446049250313e-16 relative error = 3.599876375879147e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10006 y[1] (analytic) = 0.6168160476186754 y[1] (numeric) = 0.6168160476186755 absolute error = 1.110223024625157e-16 relative error = 1.799925648678182e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10007 y[1] (analytic) = 0.6168203446739489 y[1] (numeric) = 0.6168203446739486 absolute error = 2.220446049250313e-16 relative error = 3.59982621913037e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10008 y[1] (analytic) = 0.6168246417382391 y[1] (numeric) = 0.6168246417382388 absolute error = 3.33066907387547e-16 relative error = 5.399701711801748e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10009 y[1] (analytic) = 0.6168289388115461 y[1] (numeric) = 0.6168289388115461 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001 y[1] (analytic) = 0.6168332358938703 y[1] (numeric) = 0.6168332358938704 absolute error = 1.110223024625157e-16 relative error = 1.799875493116549e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10011 y[1] (analytic) = 0.6168375329852117 y[1] (numeric) = 0.6168375329852116 absolute error = 1.110223024625157e-16 relative error = 1.799862954597112e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10012 y[1] (analytic) = 0.61684183008557 y[1] (numeric) = 0.6168418300855698 absolute error = 2.220446049250313e-16 relative error = 3.599700832452116e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10013 y[1] (analytic) = 0.6168461271949448 y[1] (numeric) = 0.6168461271949449 absolute error = 1.110223024625157e-16 relative error = 1.799837878003386e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10014 y[1] (analytic) = 0.616850424313337 y[1] (numeric) = 0.6168504243133369 absolute error = 1.110223024625157e-16 relative error = 1.799825339929092e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001499999999999 y[1] (analytic) = 0.6168547214407458 y[1] (numeric) = 0.6168547214407458 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001599999999999 y[1] (analytic) = 0.6168590185771716 y[1] (numeric) = 0.6168590185771715 absolute error = 1.110223024625157e-16 relative error = 1.799800264225631e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001699999999999 y[1] (analytic) = 0.6168633157226138 y[1] (numeric) = 0.616863315722614 absolute error = 2.220446049250313e-16 relative error = 3.599575453192917e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001799999999999 y[1] (analytic) = 0.6168676128770731 y[1] (numeric) = 0.6168676128770733 absolute error = 1.110223024625157e-16 relative error = 1.799775189115654e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001899999999999 y[1] (analytic) = 0.6168719100405492 y[1] (numeric) = 0.6168719100405493 absolute error = 1.110223024625157e-16 relative error = 1.799762651783216e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001999999999999 y[1] (analytic) = 0.6168762072130421 y[1] (numeric) = 0.616876207213042 absolute error = 1.110223024625157e-16 relative error = 1.799750114599142e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002099999999999 y[1] (analytic) = 0.6168805043945517 y[1] (numeric) = 0.6168805043945514 absolute error = 2.220446049250313e-16 relative error = 3.599475155126857e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002199999999999 y[1] (analytic) = 0.6168848015850775 y[1] (numeric) = 0.6168848015850775 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) = 0.6168890987846201 y[1] (numeric) = 0.6168890987846203 absolute error = 2.220446049250313e-16 relative error = 3.599425007874158e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002399999999999 y[1] (analytic) = 0.6168933959931796 y[1] (numeric) = 0.6168933959931796 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002499999999999 y[1] (analytic) = 0.6168976932107554 y[1] (numeric) = 0.6168976932107555 absolute error = 1.110223024625157e-16 relative error = 1.799687430904143e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002599999999999 y[1] (analytic) = 0.6169019904373478 y[1] (numeric) = 0.6169019904373479 absolute error = 1.110223024625157e-16 relative error = 1.7996748946102e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002699999999999 y[1] (analytic) = 0.6169062876729572 y[1] (numeric) = 0.616906287672957 absolute error = 2.220446049250313e-16 relative error = 3.599324716929205e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002799999999999 y[1] (analytic) = 0.6169105849175823 y[1] (numeric) = 0.6169105849175824 absolute error = 1.110223024625157e-16 relative error = 1.799649822467351e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002899999999999 y[1] (analytic) = 0.6169148821712245 y[1] (numeric) = 0.6169148821712244 absolute error = 1.110223024625157e-16 relative error = 1.799637286618439e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002999999999999 y[1] (analytic) = 0.6169191794338826 y[1] (numeric) = 0.6169191794338827 absolute error = 1.110223024625157e-16 relative error = 1.799624750917868e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003099999999999 y[1] (analytic) = 0.6169234767055572 y[1] (numeric) = 0.6169234767055575 absolute error = 2.220446049250313e-16 relative error = 3.599224430731267e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003199999999999 y[1] (analytic) = 0.6169277739862485 y[1] (numeric) = 0.6169277739862485 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003299999999999 y[1] (analytic) = 0.6169320712759561 y[1] (numeric) = 0.616932071275956 absolute error = 1.110223024625157e-16 relative error = 1.799587144706162e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003399999999999 y[1] (analytic) = 0.6169363685746798 y[1] (numeric) = 0.6169363685746797 absolute error = 1.110223024625157e-16 relative error = 1.799574609598923e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003499999999999 y[1] (analytic) = 0.6169406658824198 y[1] (numeric) = 0.6169406658824198 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) = 0.6169449631991762 y[1] (numeric) = 0.6169449631991761 absolute error = 1.110223024625157e-16 relative error = 1.799549539829421e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003699999999999 y[1] (analytic) = 0.6169492605249486 y[1] (numeric) = 0.6169492605249487 absolute error = 1.110223024625157e-16 relative error = 1.799537005167154e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003799999999999 y[1] (analytic) = 0.6169535578597375 y[1] (numeric) = 0.6169535578597374 absolute error = 1.110223024625157e-16 relative error = 1.799524470653206e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003899999999999 y[1] (analytic) = 0.6169578552035424 y[1] (numeric) = 0.6169578552035423 absolute error = 1.110223024625157e-16 relative error = 1.799511936287576e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003999999999999 y[1] (analytic) = 0.6169621525563634 y[1] (numeric) = 0.6169621525563633 absolute error = 1.110223024625157e-16 relative error = 1.79949940207026e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004099999999998 y[1] (analytic) = 0.6169664499182006 y[1] (numeric) = 0.6169664499182005 absolute error = 1.110223024625157e-16 relative error = 1.799486868001256e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004199999999998 y[1] (analytic) = 0.6169707472890537 y[1] (numeric) = 0.6169707472890538 absolute error = 1.110223024625157e-16 relative error = 1.799474334080562e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004299999999998 y[1] (analytic) = 0.6169750446689229 y[1] (numeric) = 0.6169750446689231 absolute error = 1.110223024625157e-16 relative error = 1.799461800308175e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004399999999998 y[1] (analytic) = 0.6169793420578081 y[1] (numeric) = 0.6169793420578084 absolute error = 2.220446049250313e-16 relative error = 3.598898533368185e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004499999999998 y[1] (analytic) = 0.6169836394557097 y[1] (numeric) = 0.6169836394557097 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004599999999998 y[1] (analytic) = 0.6169879368626269 y[1] (numeric) = 0.616987936862627 absolute error = 1.110223024625157e-16 relative error = 1.79942419988083e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004699999999998 y[1] (analytic) = 0.61699223427856 y[1] (numeric) = 0.6169922342785602 absolute error = 2.220446049250313e-16 relative error = 3.598823333403294e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004799999999998 y[1] (analytic) = 0.6169965317035093 y[1] (numeric) = 0.6169965317035093 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004899999999998 y[1] (analytic) = 0.6170008291374739 y[1] (numeric) = 0.6170008291374743 absolute error = 4.440892098500626e-16 relative error = 7.197546403152647e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004999999999998 y[1] (analytic) = 0.6170051265804551 y[1] (numeric) = 0.6170051265804551 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005099999999998 y[1] (analytic) = 0.6170094240324517 y[1] (numeric) = 0.6170094240324518 absolute error = 1.110223024625157e-16 relative error = 1.799361535467834e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005199999999998 y[1] (analytic) = 0.6170137214934641 y[1] (numeric) = 0.6170137214934643 absolute error = 2.220446049250313e-16 relative error = 3.598698006060201e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005299999999998 y[1] (analytic) = 0.6170180189634925 y[1] (numeric) = 0.6170180189634926 absolute error = 1.110223024625157e-16 relative error = 1.799336470740647e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005399999999998 y[1] (analytic) = 0.6170223164425365 y[1] (numeric) = 0.6170223164425366 absolute error = 1.110223024625157e-16 relative error = 1.799323938599475e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005499999999998 y[1] (analytic) = 0.617026613930596 y[1] (numeric) = 0.6170266139305962 absolute error = 2.220446049250313e-16 relative error = 3.598622813213162e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005599999999998 y[1] (analytic) = 0.6170309114276715 y[1] (numeric) = 0.6170309114276715 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) = 0.6170352089337624 y[1] (numeric) = 0.6170352089337625 absolute error = 1.110223024625157e-16 relative error = 1.799286343065614e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005799999999998 y[1] (analytic) = 0.617039506448869 y[1] (numeric) = 0.6170395064488692 absolute error = 2.220446049250313e-16 relative error = 3.598547623035075e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005899999999998 y[1] (analytic) = 0.6170438039729914 y[1] (numeric) = 0.6170438039729914 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005999999999998 y[1] (analytic) = 0.6170481015061291 y[1] (numeric) = 0.6170481015061292 absolute error = 1.110223024625157e-16 relative error = 1.799248748866184e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006099999999998 y[1] (analytic) = 0.6170523990482824 y[1] (numeric) = 0.6170523990482826 absolute error = 2.220446049250313e-16 relative error = 3.598472435525804e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006199999999998 y[1] (analytic) = 0.6170566965994512 y[1] (numeric) = 0.6170566965994514 absolute error = 2.220446049250313e-16 relative error = 3.598447373615762e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006299999999998 y[1] (analytic) = 0.6170609941596354 y[1] (numeric) = 0.6170609941596357 absolute error = 2.220446049250313e-16 relative error = 3.598422312002235e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006399999999998 y[1] (analytic) = 0.6170652917288354 y[1] (numeric) = 0.6170652917288354 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006499999999998 y[1] (analytic) = 0.6170695893070505 y[1] (numeric) = 0.6170695893070506 absolute error = 1.110223024625157e-16 relative error = 1.799186094832354e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006599999999997 y[1] (analytic) = 0.6170738868942809 y[1] (numeric) = 0.6170738868942811 absolute error = 2.220446049250313e-16 relative error = 3.598347128940698e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006699999999997 y[1] (analytic) = 0.6170781844905271 y[1] (numeric) = 0.617078184490527 absolute error = 1.110223024625157e-16 relative error = 1.799161034256592e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006799999999997 y[1] (analytic) = 0.6170824820957883 y[1] (numeric) = 0.6170824820957882 absolute error = 1.110223024625157e-16 relative error = 1.79914850419108e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006899999999997 y[1] (analytic) = 0.6170867797100649 y[1] (numeric) = 0.6170867797100648 absolute error = 1.110223024625157e-16 relative error = 1.799135974273812e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006999999999997 y[1] (analytic) = 0.6170910773333564 y[1] (numeric) = 0.6170910773333566 absolute error = 1.110223024625157e-16 relative error = 1.799123444504784e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007099999999997 y[1] (analytic) = 0.6170953749656636 y[1] (numeric) = 0.6170953749656636 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007199999999997 y[1] (analytic) = 0.6170996726069859 y[1] (numeric) = 0.6170996726069858 absolute error = 1.110223024625157e-16 relative error = 1.79909838541144e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007299999999997 y[1] (analytic) = 0.6171039702573234 y[1] (numeric) = 0.6171039702573233 absolute error = 1.110223024625157e-16 relative error = 1.799085856087119e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007399999999997 y[1] (analytic) = 0.6171082679166757 y[1] (numeric) = 0.6171082679166759 absolute error = 2.220446049250313e-16 relative error = 3.598146653822058e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007499999999997 y[1] (analytic) = 0.6171125655850438 y[1] (numeric) = 0.6171125655850437 absolute error = 1.110223024625157e-16 relative error = 1.799060797883166e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007599999999997 y[1] (analytic) = 0.6171168632624263 y[1] (numeric) = 0.6171168632624265 absolute error = 2.220446049250313e-16 relative error = 3.598096538007061e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007699999999997 y[1] (analytic) = 0.6171211609488243 y[1] (numeric) = 0.6171211609488244 absolute error = 1.110223024625157e-16 relative error = 1.799035740272117e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007799999999997 y[1] (analytic) = 0.6171254586442373 y[1] (numeric) = 0.6171254586442374 absolute error = 1.110223024625157e-16 relative error = 1.799023211688925e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007899999999997 y[1] (analytic) = 0.6171297563486653 y[1] (numeric) = 0.6171297563486654 absolute error = 1.110223024625157e-16 relative error = 1.799010683253951e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007999999999997 y[1] (analytic) = 0.6171340540621085 y[1] (numeric) = 0.6171340540621083 absolute error = 2.220446049250313e-16 relative error = 3.597996309934384e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008099999999997 y[1] (analytic) = 0.617138351784566 y[1] (numeric) = 0.6171383517845662 absolute error = 2.220446049250313e-16 relative error = 3.597971253657297e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008199999999997 y[1] (analytic) = 0.6171426495160391 y[1] (numeric) = 0.617142649516039 absolute error = 1.110223024625157e-16 relative error = 1.798973098838314e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008299999999997 y[1] (analytic) = 0.6171469472565266 y[1] (numeric) = 0.6171469472565267 absolute error = 1.110223024625157e-16 relative error = 1.79896057099619e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008399999999997 y[1] (analytic) = 0.6171512450060295 y[1] (numeric) = 0.6171512450060294 absolute error = 1.110223024625157e-16 relative error = 1.79894804330227e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008499999999997 y[1] (analytic) = 0.6171555427645469 y[1] (numeric) = 0.6171555427645468 absolute error = 1.110223024625157e-16 relative error = 1.798935515756555e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008599999999997 y[1] (analytic) = 0.6171598405320792 y[1] (numeric) = 0.6171598405320791 absolute error = 1.110223024625157e-16 relative error = 1.79892298835904e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008699999999997 y[1] (analytic) = 0.6171641383086263 y[1] (numeric) = 0.617164138308626 absolute error = 2.220446049250313e-16 relative error = 3.597820922219448e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008799999999997 y[1] (analytic) = 0.6171684360941878 y[1] (numeric) = 0.6171684360941878 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008899999999997 y[1] (analytic) = 0.6171727338887641 y[1] (numeric) = 0.6171727338887644 absolute error = 2.220446049250313e-16 relative error = 3.597770814111361e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008999999999997 y[1] (analytic) = 0.6171770316923553 y[1] (numeric) = 0.6171770316923556 absolute error = 3.33066907387547e-16 relative error = 5.396618640752838e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009099999999997 y[1] (analytic) = 0.6171813295049616 y[1] (numeric) = 0.6171813295049615 absolute error = 1.110223024625157e-16 relative error = 1.798860353594399e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009199999999996 y[1] (analytic) = 0.617185627326582 y[1] (numeric) = 0.617185627326582 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009299999999996 y[1] (analytic) = 0.6171899251572168 y[1] (numeric) = 0.6171899251572172 absolute error = 3.33066907387547e-16 relative error = 5.396505902177596e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009399999999996 y[1] (analytic) = 0.6171942229968667 y[1] (numeric) = 0.6171942229968669 absolute error = 2.220446049250313e-16 relative error = 3.597645549027742e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009499999999996 y[1] (analytic) = 0.6171985208455311 y[1] (numeric) = 0.6171985208455312 absolute error = 1.110223024625157e-16 relative error = 1.798810248450056e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009599999999996 y[1] (analytic) = 0.6172028187032096 y[1] (numeric) = 0.6172028187032099 absolute error = 3.33066907387547e-16 relative error = 5.396393167603253e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009699999999996 y[1] (analytic) = 0.6172071165699029 y[1] (numeric) = 0.6172071165699032 absolute error = 3.33066907387547e-16 relative error = 5.396355590300859e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009799999999996 y[1] (analytic) = 0.6172114144456109 y[1] (numeric) = 0.617211414445611 absolute error = 1.110223024625157e-16 relative error = 1.798772671147659e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009899999999996 y[1] (analytic) = 0.6172157123303328 y[1] (numeric) = 0.6172157123303331 absolute error = 3.33066907387547e-16 relative error = 5.396280437029609e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009999999999996 y[1] (analytic) = 0.6172200102240691 y[1] (numeric) = 0.6172200102240697 absolute error = 5.551115123125783e-16 relative error = 8.993738101767898e-14 % Correct digits = 15 h = 1e-05 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = arctan(sqrt(0.1 * x + 0.2)); Iterations = 100 Total Elapsed Time = 24 Seconds Elapsed Time(since restart) = 23 Seconds Expected Time Remaining = 2 Hours 38 Minutes 0 Seconds Optimized Time Remaining = 2 Hours 31 Minutes 25 Seconds Time to Timeout = 36 Seconds Percent Done = 0.2525 %