##############ECHO OF PROBLEM################# ##############temp/lin_lnpostode.ode################# diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=20.0 x_end=30.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_min_h=0.001 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=-2.0 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=1.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=0.0 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=16 $glob_max_minutes=3.0 $glob_subiter_method=3 $glob_max_iter=100000000 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(10.0* (0.1 * x + 0.2) * ln(0.1 * x + 0.2) - x - 2.0) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.001 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 10.0 estimated_steps 10000.0 step_error 3.3333333333333337e-20 est_needed_step_err 3.3333333333333337e-20 opt_iter 1 Radius of convergence (given) for eq 1 22.0 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 22.00000000000018 Order of pole (three term test) 0.9999999999998785 NO COMPLEX POLE (six term test) for Equation 1 min_size 4.653938071986055 $glob_desired_digits_correct 16 estimated_h 0.001 estimated_answer 4.653938071986055 desired_abs_gbl_error 4.653938071986055e-16 range 10.0 estimated_steps 10000.0 step_error 1.551312690662018e-19 est_needed_step_err 1.551312690662018e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.231657246543749e-115 estimated_step_error 4.231657246543749e-115 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 22.0 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 22.00000000000018 Order of pole (three term test) 0.9999999999998785 NO COMPLEX POLE (six term test) for Equation 1 min_size 4.653938071986055 $glob_desired_digits_correct 16 estimated_h 0.002 estimated_answer 4.653938071986055 desired_abs_gbl_error 4.653938071986055e-16 range 10.0 estimated_steps 5000.0 step_error 2.193887446615724e-19 est_needed_step_err 2.193887446615724e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.839757348594036e-107 estimated_step_error 2.839757348594036e-107 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 22.0 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 22.00000000000018 Order of pole (three term test) 0.9999999999998785 NO COMPLEX POLE (six term test) for Equation 1 min_size 4.653938071986055 $glob_desired_digits_correct 16 estimated_h 0.004 estimated_answer 4.653938071986055 desired_abs_gbl_error 4.653938071986055e-16 range 10.0 estimated_steps 2500.0 step_error 3.102625381324036e-19 est_needed_step_err 3.102625381324036e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.9056486963326453e-99 estimated_step_error 1.9056486963326453e-99 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 22.0 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 22.00000000000018 Order of pole (three term test) 0.9999999999998785 NO COMPLEX POLE (six term test) for Equation 1 min_size 4.653938071986055 $glob_desired_digits_correct 16 estimated_h 0.008 estimated_answer 4.653938071986055 desired_abs_gbl_error 4.653938071986055e-16 range 10.0 estimated_steps 1250.0 step_error 4.387774893231448e-19 est_needed_step_err 4.387774893231448e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2787515620566715e-91 estimated_step_error 1.2787515620566715e-91 Double H and LOOP opt_iter 5 Radius of convergence (given) for eq 1 22.0 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 22.00000000000018 Order of pole (three term test) 0.9999999999998785 NO COMPLEX POLE (six term test) for Equation 1 min_size 4.653938071986055 $glob_desired_digits_correct 16 estimated_h 0.016 estimated_answer 4.653938071986055 desired_abs_gbl_error 4.653938071986055e-16 range 10.0 estimated_steps 625.0 step_error 6.205250762648072e-19 est_needed_step_err 6.205250762648072e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.580112248661087e-84 estimated_step_error 8.580112248661087e-84 Double H and LOOP opt_iter 6 Radius of convergence (given) for eq 1 22.0 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 22.00000000000018 Order of pole (three term test) 0.9999999999998785 NO COMPLEX POLE (six term test) for Equation 1 min_size 4.653938071986055 $glob_desired_digits_correct 16 estimated_h 0.032 estimated_answer 4.653938071986055 desired_abs_gbl_error 4.653938071986055e-16 range 10.0 estimated_steps 312.5 step_error 8.775549786462896e-19 est_needed_step_err 8.775549786462896e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.756078444366932e-76 estimated_step_error 5.756078444366932e-76 Double H and LOOP opt_iter 7 Radius of convergence (given) for eq 1 22.0 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 22.00000000000018 Order of pole (three term test) 0.9999999999998785 NO COMPLEX POLE (six term test) for Equation 1 min_size 4.653938071986055 $glob_desired_digits_correct 16 estimated_h 0.064 estimated_answer 4.653938071986055 desired_abs_gbl_error 4.653938071986055e-16 range 10.0 estimated_steps 156.25 step_error 1.2410501525296145e-18 est_needed_step_err 1.2410501525296145e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.860241130263208e-68 estimated_step_error 3.860241130263208e-68 Double H and LOOP opt_iter 8 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 22.0 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 17.187500000000142 Order of pole (three term test) 0.9999999999998785 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] 20.0 y[1] (closed_form) -4.653938071986055 y[1] (numeric) -4.653938071986055 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 22.0 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 21.99999999999995 Order of pole (three term test) 1.0000000000000393 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 20.1 y[1] (closed_form) -4.574865406794476 y[1] (numeric) -4.574865406794481 absolute error 4.440892098500626e-15 relative error 9.707153552332105e-14% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 22.1 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 22.099999999999675 Order of pole (three term test) 1.0000000000001628 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 20.200000000000003 y[1] (closed_form) -4.495340251371015 y[1] (numeric) -4.495340251371023 absolute error 7.993605777301127e-15 relative error 1.7781981630563317e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 22.200000000000003 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 22.199999999999854 Order of pole (three term test) 1.000000000000147 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 20.300000000000004 y[1] (closed_form) -4.415364643973778 y[1] (numeric) -4.4153646439737875 absolute error 9.769962616701378e-15 relative error 2.2127193118773815e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 22.300000000000004 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 22.29999999999979 Order of pole (three term test) 1.0000000000000921 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 20.400000000000006 y[1] (closed_form) -4.33494060458035 y[1] (numeric) -4.3349406045803525 absolute error 2.6645352591003757e-15 relative error 6.146647675599052e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 22.400000000000006 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 22.400000000000055 Order of pole (three term test) 0.9999999999998784 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 20.500000000000007 y[1] (closed_form) -4.254070135132594 y[1] (numeric) -4.254070135132602 absolute error 7.993605777301127e-15 relative error 1.879048892796869e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 22.500000000000007 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 22.499999999999922 Order of pole (three term test) 1.0000000000001 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 20.60000000000001 y[1] (closed_form) -4.172755219777191 y[1] (numeric) -4.172755219777203 absolute error 1.2434497875801753e-14 relative error 2.97992506650455e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 22.60000000000001 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 22.59999999999975 Order of pole (three term test) 1.0000000000002824 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 20.70000000000001 y[1] (closed_form) -4.0909978251018195 y[1] (numeric) -4.090997825101832 absolute error 1.2434497875801753e-14 relative error 3.039477997153977e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 22.70000000000001 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 22.699999999999896 Order of pole (three term test) 1.000000000000121 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 20.80000000000001 y[1] (closed_form) -4.008799900367215 y[1] (numeric) -4.008799900367232 absolute error 1.687538997430238e-14 relative error 4.2095865081109576e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 22.80000000000001 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 22.80000000000012 Order of pole (three term test) 0.9999999999998991 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 20.900000000000013 y[1] (closed_form) -3.926163377735193 y[1] (numeric) -3.926163377735203 absolute error 9.769962616701378e-15 relative error 2.4884248760776683e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 22.900000000000013 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 22.89999999999982 Order of pole (three term test) 1.0000000000001807 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 21.000000000000014 y[1] (closed_form) -3.8430901724925945 y[1] (numeric) -3.8430901724926065 absolute error 1.199040866595169e-14 relative error 3.119991498449493e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 23.000000000000014 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 22.999999999999787 Order of pole (three term test) 1.0000000000001157 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 21.100000000000016 y[1] (closed_form) -3.759582183271462 y[1] (numeric) -3.7595821832714784 absolute error 1.6431300764452317e-14 relative error 4.3705124568268786e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 23.100000000000016 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 23.099999999999895 Order of pole (three term test) 1.0000000000000417 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 21.200000000000017 y[1] (closed_form) -3.6756412922653077 y[1] (numeric) -3.675641292265327 absolute error 1.9539925233402755e-14 relative error 5.316058798915127e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 23.200000000000017 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 23.19999999999981 Order of pole (three term test) 1.0000000000002292 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 21.30000000000002 y[1] (closed_form) -3.5912693654416827 y[1] (numeric) -3.591269365441704 absolute error 2.1316282072803006e-14 relative error 5.935584302844785e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 23.30000000000002 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 23.300000000000036 Order of pole (three term test) 1.0000000000000497 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 21.40000000000002 y[1] (closed_form) -3.506468252751109 y[1] (numeric) -3.506468252751123 absolute error 1.4210854715202004e-14 relative error 4.05275442150444e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 23.40000000000002 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 23.400000000000002 Order of pole (three term test) 1.000000000000095 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 21.50000000000002 y[1] (closed_form) -3.421239788332393 y[1] (numeric) -3.42123978833241 absolute error 1.687538997430238e-14 relative error 4.932536454139601e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 23.50000000000002 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 23.499999999999837 Order of pole (three term test) 1.0000000000001175 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 21.600000000000023 y[1] (closed_form) -3.335585790714532 y[1] (numeric) -3.335585790714557 absolute error 2.4868995751603507e-14 relative error 7.455660658116726e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 23.600000000000023 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 23.59999999999987 Order of pole (three term test) 1.0000000000002738 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 21.700000000000024 y[1] (closed_form) -3.249508063015128 y[1] (numeric) -3.2495080630151545 absolute error 2.6645352591003757e-14 relative error 8.199811194276674e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 23.700000000000024 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 23.699999999999918 Order of pole (three term test) 1.0000000000001965 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 21.800000000000026 y[1] (closed_form) -3.163008393135449 y[1] (numeric) -3.163008393135475 absolute error 2.5757174171303632e-14 relative error 8.143251920293161e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 23.800000000000026 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 23.79999999999983 Order of pole (three term test) 1.0000000000000981 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 21.900000000000027 y[1] (closed_form) -3.0760885539522533 y[1] (numeric) -3.076088553952277 absolute error 2.353672812205332e-14 relative error 7.651511882456247e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 23.900000000000027 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 23.899999999999828 Order of pole (three term test) 1.0000000000001188 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 22.00000000000003 y[1] (closed_form) -2.988750303506375 y[1] (numeric) -2.9887503035063996 absolute error 2.4424906541753444e-14 relative error 8.17228073991272e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 Radius of convergence (given) for eq 1 24.00000000000003 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 23.999999999999968 Order of pole (three term test) 1.000000000000197 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 22.10000000000003 y[1] (closed_form) -2.9009953851881853 y[1] (numeric) -2.9009953851882146 absolute error 2.930988785010413e-14 relative error 1.0103390029420134e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 24.10000000000003 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 24.099999999999987 Order of pole (three term test) 1.0000000000000706 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 22.20000000000003 y[1] (closed_form) -2.8128255279199657 y[1] (numeric) -2.812825527919998 absolute error 3.241851231905457e-14 relative error 1.152524818808349e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 24.20000000000003 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 24.199999999999978 Order of pole (three term test) 1.00000000000005 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 22.300000000000033 y[1] (closed_form) -2.7242424463352535 y[1] (numeric) -2.7242424463352903 absolute error 3.68594044175552e-14 relative error 1.353014834165724e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 24.300000000000033 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 24.30000000000009 Order of pole (three term test) 0.9999999999999176 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 22.400000000000034 y[1] (closed_form) -2.635247840955273 y[1] (numeric) -2.635247840955301 absolute error 2.7977620220553945e-14 relative error 1.0616694105861445e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 24.400000000000034 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 24.399999999999995 Order of pole (three term test) 1.000000000000072 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 22.500000000000036 y[1] (closed_form) -2.5458433983623934 y[1] (numeric) -2.5458433983624245 absolute error 3.108624468950438e-14 relative error 1.2210587936988002e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 24.500000000000036 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 24.499999999999794 Order of pole (three term test) 1.0000000000001759 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 22.600000000000037 y[1] (closed_form) -2.4560307913708854 y[1] (numeric) -2.4560307913709196 absolute error 3.419486915845482e-14 relative error 1.3922817775166506e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 24.600000000000037 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 24.599999999999817 Order of pole (three term test) 1.000000000000266 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 22.70000000000004 y[1] (closed_form) -2.3658116791947776 y[1] (numeric) -2.3658116791948167 absolute error 3.907985046680551e-14 relative error 1.6518580413850455e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 24.70000000000004 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 24.70000000000002 Order of pole (three term test) 1.0000000000000953 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 22.80000000000004 y[1] (closed_form) -2.275187707613064 y[1] (numeric) -2.2751877076131044 absolute error 4.04121180963557e-14 relative error 1.7762102863483163e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 24.80000000000004 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 24.79999999999991 Order of pole (three term test) 1.0000000000000668 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 22.90000000000004 y[1] (closed_form) -2.1841605091322194 y[1] (numeric) -2.184160509132252 absolute error 3.241851231905457e-14 relative error 1.4842550345319927e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 24.90000000000004 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 24.899999999999785 Order of pole (three term test) 1.000000000000285 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 23.000000000000043 y[1] (closed_form) -2.0927317031460824 y[1] (numeric) -2.0927317031461197 absolute error 3.730349362740526e-14 relative error 1.7825263301227535e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 25.000000000000043 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 25.00000000000001 Order of pole (three term test) 1.000000000000002 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 23.100000000000044 y[1] (closed_form) -2.0009028960932724 y[1] (numeric) -2.0009028960933137 absolute error 4.1300296516055823e-14 relative error 2.0640829995645427e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 25.100000000000044 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 25.10000000000011 Order of pole (three term test) 0.9999999999998973 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 23.200000000000045 y[1] (closed_form) -1.9086756816119852 y[1] (numeric) -1.908675681612031 absolute error 4.574118861455645e-14 relative error 2.396488259122441e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 25.200000000000045 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 25.2 Order of pole (three term test) 0.9999999999999384 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 23.300000000000047 y[1] (closed_form) -1.8160516406924003 y[1] (numeric) -1.8160516406924452 absolute error 4.4853010194856324e-14 relative error 2.4698091832760526e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 25.300000000000047 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 25.299999999999773 Order of pole (three term test) 1.0000000000002383 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 23.40000000000005 y[1] (closed_form) -1.723032341826645 y[1] (numeric) -1.7230323418266869 absolute error 4.1744385725905886e-14 relative error 2.422727926374919e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 25.40000000000005 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 25.39999999999995 Order of pole (three term test) 1.0000000000000426 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 23.50000000000005 y[1] (closed_form) -1.6296193411564168 y[1] (numeric) -1.6296193411564583 absolute error 4.1522341120980855e-14 relative error 2.5479779278709107e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 25.50000000000005 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 25.499999999999947 Order of pole (three term test) 1.0000000000001055 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 23.60000000000005 y[1] (closed_form) -1.5358141826182852 y[1] (numeric) -1.5358141826183347 absolute error 4.951594689828198e-14 relative error 3.224084492686886e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 25.60000000000005 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 25.59999999999975 Order of pole (three term test) 1.0000000000002385 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 23.700000000000053 y[1] (closed_form) -1.4416183980867423 y[1] (numeric) -1.4416183980867943 absolute error 5.1958437552457326e-14 relative error 3.604174143546896e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 25.700000000000053 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 25.699999999999815 Order of pole (three term test) 1.0000000000001694 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 23.800000000000054 y[1] (closed_form) -1.3470335075149684 y[1] (numeric) -1.3470335075150224 absolute error 5.395683899678261e-14 relative error 4.0056048120379095e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 25.800000000000054 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 25.799999999999972 Order of pole (three term test) 1.0000000000000997 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 23.900000000000055 y[1] (closed_form) -1.2520610190734835 y[1] (numeric) -1.252061019073533 absolute error 4.951594689828198e-14 relative error 3.9547550913232195e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 25.900000000000055 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 25.8999999999998 Order of pole (three term test) 1.000000000000198 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 24.000000000000057 y[1] (closed_form) -1.1567024292866002 y[1] (numeric) -1.1567024292866488 absolute error 4.8627768478581856e-14 relative error 4.203999857471829e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 26.000000000000057 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 25.999999999999883 Order of pole (three term test) 1.000000000000105 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 24.10000000000006 y[1] (closed_form) -1.060959223166826 y[1] (numeric) -1.0609592231668807 absolute error 5.484501741648273e-14 relative error 5.169380332335248e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 26.10000000000006 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 26.099999999999966 Order of pole (three term test) 1.0000000000000946 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 24.20000000000006 y[1] (closed_form) -0.9648328743471914 y[1] (numeric) -0.9648328743472501 absolute error 5.861977570020827e-14 relative error 6.075640378637654e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 26.20000000000006 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 26.19999999999993 Order of pole (three term test) 1.0000000000002016 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 24.30000000000006 y[1] (closed_form) -0.8683248452115286 y[1] (numeric) -0.8683248452115888 absolute error 6.017408793468348e-14 relative error 6.929905123240456e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 26.30000000000006 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 26.299999999999795 Order of pole (three term test) 1.0000000000001208 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 24.400000000000063 y[1] (closed_form) -0.7714365870227908 y[1] (numeric) -0.7714365870228587 absolute error 6.783462680459706e-14 relative error 8.793286181355695e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 26.400000000000063 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 26.39999999999977 Order of pole (three term test) 1.0000000000001623 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 24.500000000000064 y[1] (closed_form) -0.6741695400494692 y[1] (numeric) -0.6741695400495258 absolute error 5.6621374255882984e-14 relative error 8.398684736146374e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 26.500000000000064 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 26.499999999999925 Order of pole (three term test) 1.0000000000001394 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 24.600000000000065 y[1] (closed_form) -0.5765251336899624 y[1] (numeric) -0.5765251336900278 absolute error 6.539213615042172e-14 relative error 1.1342460602175172e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.1 Radius of convergence (given) for eq 1 26.600000000000065 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 26.600000000000172 Order of pole (three term test) 0.9999999999999142 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 24.700000000000067 y[1] (closed_form) -0.4785047865953018 y[1] (numeric) -0.4785047865953696 absolute error 6.777911565336581e-14 relative error 1.416477275716165e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.1 Radius of convergence (given) for eq 1 26.700000000000067 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 26.6999999999998 Order of pole (three term test) 1.000000000000225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 24.800000000000068 y[1] (closed_form) -0.38010990678981216 y[1] (numeric) -0.38010990678988194 absolute error 6.977751709769109e-14 relative error 1.8357195077337375e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.1 Radius of convergence (given) for eq 1 26.800000000000068 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 26.79999999999975 Order of pole (three term test) 1.0000000000001084 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 24.90000000000007 y[1] (closed_form) -0.28134189179010605 y[1] (numeric) -0.2813418917901778 absolute error 7.177591854201637e-14 relative error 2.551199115258829e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.1 Radius of convergence (given) for eq 1 26.90000000000007 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 26.899999999999935 Order of pole (three term test) 1.0000000000001854 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 25.00000000000007 y[1] (closed_form) -0.18220212872227393 y[1] (numeric) -0.18220212872234015 absolute error 6.622480341889059e-14 relative error 3.634688786750421e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.1 Radius of convergence (given) for eq 1 27.00000000000007 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 26.99999999999991 Order of pole (three term test) 1.0000000000000249 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 25.100000000000072 y[1] (closed_form) -0.08269199443730102 y[1] (numeric) -0.08269199443737309 absolute error 7.206735208598047e-14 relative error 8.715154662356537e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.1 Radius of convergence (given) for eq 1 27.100000000000072 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 27.099999999999984 Order of pole (three term test) 1.0000000000001126 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 25.200000000000074 y[1] (closed_form) 0.01718714437512503 y[1] (numeric) 0.017187144375050714 absolute error 7.431555371084642e-14 relative error 4.3239034995483827e-10% Desired digits 16 Estimated correct digits 10 Correct digits 12 h 0.1 Radius of convergence (given) for eq 1 27.200000000000074 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 27.19999999999982 Order of pole (three term test) 1.000000000000177 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 25.300000000000075 y[1] (closed_form) 0.11743393107458999 y[1] (numeric) 0.11743393107451552 absolute error 7.446820937673237e-14 relative error 6.341285580351793e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.1 Radius of convergence (given) for eq 1 27.300000000000075 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 27.29999999999978 Order of pole (three term test) 1.0000000000002283 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 25.400000000000077 y[1] (closed_form) 0.21804701895950984 y[1] (numeric) 0.21804701895943013 absolute error 7.971401316808624e-14 relative error 3.655817609819683e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.1 Radius of convergence (given) for eq 1 27.400000000000077 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 27.399999999999864 Order of pole (three term test) 1.0000000000000744 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 25.500000000000078 y[1] (closed_form) 0.3190250711582756 y[1] (numeric) 0.31902507115820766 absolute error 6.794564910705958e-14 relative error 2.129790265710816e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.1 Radius of convergence (given) for eq 1 27.500000000000078 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 27.499999999999975 Order of pole (three term test) 1.000000000000161 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 25.60000000000008 y[1] (closed_form) 0.42036676052210353 y[1] (numeric) 0.42036676052202826 absolute error 7.527312106958561e-14 relative error 1.7906534992465854e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.1 Radius of convergence (given) for eq 1 27.60000000000008 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 27.599999999999905 Order of pole (three term test) 1.0000000000001048 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 25.70000000000008 y[1] (closed_form) 0.5220707695192388 y[1] (numeric) 0.5220707695191559 absolute error 8.293365993949919e-14 relative error 1.588552065764391e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.1 Radius of convergence (given) for eq 1 27.70000000000008 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 27.699999999999697 Order of pole (three term test) 1.0000000000002451 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 25.800000000000082 y[1] (closed_form) 0.6241357901308646 y[1] (numeric) 0.624135790130781 absolute error 8.359979375427429e-14 relative error 1.3394488038691972e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.1 Radius of convergence (given) for eq 1 27.800000000000082 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 27.800000000000125 Order of pole (three term test) 0.9999999999999755 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 25.900000000000084 y[1] (closed_form) 0.7265605237484465 y[1] (numeric) 0.7265605237483628 absolute error 8.37108160567368e-14 relative error 1.1521520000131413e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.1 Radius of convergence (given) for eq 1 27.900000000000084 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 27.899999999999874 Order of pole (three term test) 1.0000000000000469 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 26.000000000000085 y[1] (closed_form) 0.8293436810725225 y[1] (numeric) 0.8293436810724419 absolute error 8.060219158778636e-14 relative error 9.71879251356327e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 28.000000000000085 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 27.999999999999982 Order of pole (three term test) 1.0000000000001288 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 26.100000000000087 y[1] (closed_form) 0.932483982012986 y[1] (numeric) 0.9324839820129001 absolute error 8.593126210598712e-14 relative error 9.215307046935464e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 28.100000000000087 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 28.099999999999955 Order of pole (three term test) 1.000000000000129 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 26.200000000000088 y[1] (closed_form) 1.035980155590721 y[1] (numeric) 1.0359801555906385 absolute error 8.260059303211165e-14 relative error 7.973182940460126e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 28.200000000000088 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 28.200000000000056 Order of pole (three term test) 1.0000000000000018 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 26.30000000000009 y[1] (closed_form) 1.139830939840742 y[1] (numeric) 1.1398309398406512 absolute error 9.08162434143378e-14 relative error 7.967518711768494e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 28.30000000000009 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 28.30000000000047 Order of pole (three term test) 0.9999999999996715 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 26.40000000000009 y[1] (closed_form) 1.2440350817165644 y[1] (numeric) 1.2440350817164691 absolute error 9.525713551283843e-14 relative error 7.657110069709546e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 28.40000000000009 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 28.399999999999807 Order of pole (three term test) 1.0000000000002 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 26.500000000000092 y[1] (closed_form) 1.3485913369960372 y[1] (numeric) 1.3485913369959488 absolute error 8.837375276016246e-14 relative error 6.5530417062453775e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 28.500000000000092 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 28.499999999999975 Order of pole (three term test) 1.0000000000001985 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 26.600000000000094 y[1] (closed_form) 1.4534984701884746 y[1] (numeric) 1.453498470188384 absolute error 9.059419880941277e-14 relative error 6.232837575512925e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 28.600000000000094 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 28.60000000000008 Order of pole (three term test) 1.0000000000000007 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 26.700000000000095 y[1] (closed_form) 1.5587552544430103 y[1] (numeric) 1.5587552544429168 absolute error 9.348077867343818e-14 relative error 5.997142810392106e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 28.700000000000095 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 28.699999999999644 Order of pole (three term test) 1.0000000000003 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 26.800000000000097 y[1] (closed_form) 1.6643604714583233 y[1] (numeric) 1.664360471458225 absolute error 9.836575998178887e-14 relative error 5.910123538057844e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 28.800000000000097 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 28.799999999999773 Order of pole (three term test) 1.0000000000002423 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 26.900000000000098 y[1] (closed_form) 1.7703129113935638 y[1] (numeric) 1.7703129113934628 absolute error 1.0103029524088925e-13 relative error 5.706917381140248e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 28.900000000000098 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 28.899999999999938 Order of pole (three term test) 1.0000000000001 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 27.0000000000001 y[1] (closed_form) 1.876611372780527 y[1] (numeric) 1.8766113727804363 absolute error 9.059419880941277e-14 relative error 4.827541819443504e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 29.0000000000001 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 28.999999999999662 Order of pole (three term test) 1.000000000000332 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 27.1000000000001 y[1] (closed_form) 1.9832546624370906 y[1] (numeric) 1.983254662436988 absolute error 1.0258460747536446e-13 relative error 5.172538323913734e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 29.1000000000001 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 29.09999999999994 Order of pole (three term test) 1.0000000000000488 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 27.200000000000102 y[1] (closed_form) 2.0902415953816735 y[1] (numeric) 2.090241595381574 absolute error 9.947598300641403e-14 relative error 4.759066283352281e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 29.200000000000102 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 29.200000000000017 Order of pole (three term test) 0.9999999999999574 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 27.300000000000104 y[1] (closed_form) 2.197570994749114 y[1] (numeric) 2.19757099474901 absolute error 1.0391687510491465e-13 relative error 4.728715265773624e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 29.300000000000104 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 29.299999999999894 Order of pole (three term test) 1.0000000000000784 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 27.400000000000105 y[1] (closed_form) 2.305241691707483 y[1] (numeric) 2.305241691707369 absolute error 1.141309269314661e-13 relative error 4.95093106037527e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 29.400000000000105 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 29.39999999999988 Order of pole (three term test) 1.0000000000000981 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 27.500000000000107 y[1] (closed_form) 2.413252525376109 y[1] (numeric) 2.4132525253760058 absolute error 1.0302869668521453e-13 relative error 4.269287842935433e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 29.500000000000107 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 29.49999999999996 Order of pole (three term test) 1.0000000000000133 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 27.600000000000108 y[1] (closed_form) 2.5216023427448064 y[1] (numeric) 2.5216023427446994 absolute error 1.0702549957386509e-13 relative error 4.244344865946073e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 29.600000000000108 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 29.599999999999884 Order of pole (three term test) 1.0000000000000906 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 27.70000000000011 y[1] (closed_form) 2.6302899985939874 y[1] (numeric) 2.630289998593882 absolute error 1.0524914273446484e-13 relative error 4.001427325151425e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 29.70000000000011 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 29.700000000000134 Order of pole (three term test) 0.9999999999999591 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 27.80000000000011 y[1] (closed_form) 2.739314355416063 y[1] (numeric) 2.739314355415947 absolute error 1.1590728377086634e-13 relative error 4.231251646664761e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 29.80000000000011 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 29.800000000000058 Order of pole (three term test) 1.0000000000000488 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 27.900000000000112 y[1] (closed_form) 2.848674283337729 y[1] (numeric) 2.8486742833376097 absolute error 1.1945999744966684e-13 relative error 4.193529535770519e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 29.900000000000112 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 29.899999999999938 Order of pole (three term test) 1.00000000000009 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 28.000000000000114 y[1] (closed_form) 2.958368660043419 y[1] (numeric) 2.9583686600433086 absolute error 1.1057821325266559e-13 relative error 3.737810461088466e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 30.000000000000114 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 29.99999999999993 Order of pole (three term test) 1.0000000000000981 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 28.100000000000115 y[1] (closed_form) 3.0683963706997446 y[1] (numeric) 3.0683963706996273 absolute error 1.1723955140041653e-13 relative error 3.820873747601265e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 30.100000000000115 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 30.10000000000021 Order of pole (three term test) 0.9999999999998593 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 28.200000000000117 y[1] (closed_form) 3.178756307880839 y[1] (numeric) 3.178756307880722 absolute error 1.1679546219056647e-13 relative error 3.674250268918216e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 30.200000000000117 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 30.199999999999935 Order of pole (three term test) 1.0000000000001097 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 28.300000000000118 y[1] (closed_form) 3.289447371494859 y[1] (numeric) 3.2894473714947354 absolute error 1.234568003383174e-13 relative error 3.753116751711812e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 30.300000000000118 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 30.300000000000026 Order of pole (three term test) 1.0000000000000273 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 28.40000000000012 y[1] (closed_form) 3.40046846871131 y[1] (numeric) 3.4004684687111815 absolute error 1.283417816466681e-13 relative error 3.7742382506286355e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 30.40000000000012 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 30.399999999999736 Order of pole (three term test) 1.0000000000002576 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 28.50000000000012 y[1] (closed_form) 3.511818513889402 y[1] (numeric) 3.5118185138892875 absolute error 1.1457501614131615e-13 relative error 3.2625551601874286e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 30.50000000000012 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 30.50000000000014 Order of pole (three term test) 1.0000000000000073 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 28.600000000000122 y[1] (closed_form) 3.6234964285074014 y[1] (numeric) 3.6234964285072757 absolute error 1.2567724638756772e-13 relative error 3.4683971370529808e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 30.600000000000122 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 30.6 Order of pole (three term test) 1.0000000000001092 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 28.700000000000124 y[1] (closed_form) 3.7355011410926906 y[1] (numeric) 3.735501141092568 absolute error 1.2256862191861728e-13 relative error 3.2811828263225778e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 30.700000000000124 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 30.70000000000022 Order of pole (three term test) 0.9999999999999604 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 28.800000000000125 y[1] (closed_form) 3.8478315871530313 y[1] (numeric) 3.8478315871529003 absolute error 1.3100631690576847e-13 relative error 3.40467907543476e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 30.800000000000125 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 30.799999999999965 Order of pole (three term test) 1.000000000000144 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 28.900000000000126 y[1] (closed_form) 3.9604867091084657 y[1] (numeric) 3.960486709108333 absolute error 1.3278267374516872e-13 relative error 3.352685755510566e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 30.900000000000126 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 30.90000000000009 Order of pole (three term test) 1.0000000000001188 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 29.000000000000128 y[1] (closed_form) 4.0734654562242625 y[1] (numeric) 4.073465456224139 absolute error 1.234568003383174e-13 relative error 3.0307560396682682e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 31.000000000000128 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 30.999999999999876 Order of pole (three term test) 1.0000000000001972 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 29.10000000000013 y[1] (closed_form) 4.1867667845446945 y[1] (numeric) 4.186766784544562 absolute error 1.3233858453531866e-13 relative error 3.1608778646052604e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 31.10000000000013 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 31.099999999999703 Order of pole (three term test) 1.0000000000001998 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 29.20000000000013 y[1] (closed_form) 4.300389656827555 y[1] (numeric) 4.300389656827422 absolute error 1.3322676295501878e-13 relative error 3.0980160772989497e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 31.20000000000013 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 31.200000000000063 Order of pole (three term test) 1.000000000000001 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 29.300000000000132 y[1] (closed_form) 4.414333042479697 y[1] (numeric) 4.4143330424795595 absolute error 1.376676550535194e-13 relative error 3.1186513053891897e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 31.300000000000132 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 31.30000000000005 Order of pole (three term test) 1.0000000000001004 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 29.400000000000134 y[1] (closed_form) 4.528595917493256 y[1] (numeric) 4.528595917493111 absolute error 1.4477308241112041e-13 relative error 3.1968646584669808e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 31.400000000000134 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 31.400000000000066 Order of pole (three term test) 1.0000000000000737 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 29.500000000000135 y[1] (closed_form) 4.6431772643827145 y[1] (numeric) 4.643177264382588 absolute error 1.2612133559741778e-13 relative error 2.716272251005367e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 31.500000000000135 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 31.499999999999822 Order of pole (three term test) 1.0000000000001565 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 29.600000000000136 y[1] (closed_form) 4.758076072122897 y[1] (numeric) 4.758076072122761 absolute error 1.3589129821411916e-13 relative error 2.856013568389396e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 31.600000000000136 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 31.599999999999852 Order of pole (three term test) 1.0000000000001297 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 29.700000000000138 y[1] (closed_form) 4.873291336087462 y[1] (numeric) 4.873291336087325 absolute error 1.3677947663381929e-13 relative error 2.8067165946133058e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 31.700000000000138 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 31.700000000000045 Order of pole (three term test) 1.0000000000000644 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 29.80000000000014 y[1] (closed_form) 4.988822057988486 y[1] (numeric) 4.988822057988345 absolute error 1.412203687323199e-13 relative error 2.8307357346247094e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 31.80000000000014 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 31.8 Order of pole (three term test) 1.0000000000000513 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 29.90000000000014 y[1] (closed_form) 5.1046672458166 y[1] (numeric) 5.104667245816454 absolute error 1.4566126083082054e-13 relative error 2.853491791265993e-12% Desired digits 16 Estimated correct digits 13 Correct digits 14 h 0.1 Radius of convergence (given) for eq 1 31.90000000000014 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 31.900000000000023 Order of pole (three term test) 1.0000000000001088 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; Iterations 100 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 101.00000000000144%