##############ECHO OF PROBLEM################# ##############temp/sub_lin_sinpostode.ode################# diff ( y , x , 1 ) = (0.1 * x + 1.0) - sin(x); ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=5.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.1 $glob_look_poles=true $glob_max_iter=10000000 $glob_max_minutes=3 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(cos(x) + (0.05 * x * x) + x) 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 10 desired_abs_gbl_error 1.0e-10 range 4.9 estimated_steps 4900000.000000001 step_error 2.040816326530612e-17 est_needed_step_err 2.040816326530612e-17 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.467208605532302e-183 estimated_step_error 2.467208605532302e-183 best_h 2.0e-06 opt_iter 2 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.655715664606566e-175 estimated_step_error 1.655715664606566e-175 best_h 4.0e-06 opt_iter 3 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1111319694584357e-167 estimated_step_error 1.1111319694584357e-167 best_h 8.0e-06 opt_iter 4 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.456680367024187e-160 estimated_step_error 7.456680367024187e-160 best_h 1.6e-05 opt_iter 5 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.004093412037817e-152 estimated_step_error 5.004093412037817e-152 best_h 3.2e-05 opt_iter 6 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.3581901424816246e-144 estimated_step_error 3.3581901424816246e-144 best_h 6.4e-05 opt_iter 7 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.2536431215809203e-136 estimated_step_error 2.2536431215809203e-136 best_h 0.000128 opt_iter 8 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.512394117654307e-128 estimated_step_error 1.512394117654307e-128 best_h 0.000256 opt_iter 9 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0149502701580557e-120 estimated_step_error 1.0149502701580557e-120 best_h 0.000512 opt_iter 10 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.811212724408108e-113 estimated_step_error 6.811212724408108e-113 best_h 0.001024 opt_iter 11 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.5709231343600255e-105 estimated_step_error 4.5709231343600255e-105 best_h 0.002048 opt_iter 12 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.067488750234022e-97 estimated_step_error 3.067488750234022e-97 best_h 0.004096 opt_iter 13 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.0585490116180908e-89 estimated_step_error 2.0585490116180908e-89 best_h 0.008192 opt_iter 14 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3814583197402446e-81 estimated_step_error 1.3814583197402446e-81 best_h 0.016384 opt_iter 15 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.270668118428106e-74 estimated_step_error 9.270668118428106e-74 best_h 0.032768 opt_iter 16 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.221249002016116e-66 estimated_step_error 6.221249002016116e-66 best_h 0.065536 opt_iter 17 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.174750875079242e-58 estimated_step_error 4.174750875079242e-58 best_h 0.131072 opt_iter 18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.801274754399603e-50 estimated_step_error 2.801274754399603e-50 best_h 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (analytic) 1.0955041652780257 y[1] (numeric) 1.0955041652780257 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2 y[1] (analytic) 1.1820665778412416 y[1] (numeric) 1.1820665778412416 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.30000000000000004 y[1] (analytic) 1.259836489125606 y[1] (numeric) 1.259836489125606 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4 y[1] (analytic) 1.329060994002885 y[1] (numeric) 1.329060994002885 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5 y[1] (analytic) 1.3900825618903727 y[1] (numeric) 1.3900825618903727 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6 y[1] (analytic) 1.4433356149096783 y[1] (numeric) 1.4433356149096783 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7 y[1] (analytic) 1.4893421872844885 y[1] (numeric) 1.4893421872844885 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 16.845767609261582 Order of pole (ratio test) 110.8929175244212 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7999999999999999 y[1] (analytic) 1.5287067093471656 y[1] (numeric) 1.5287067093471656 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 18.453077412359015 Order of pole (ratio test) 123.00162692311689 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8999999999999999 y[1] (analytic) 1.5621099682706645 y[1] (numeric) 1.5621099682706645 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.077471809004024 Order of pole (ratio test) 97.47386984028233 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9999999999999999 y[1] (analytic) 1.5903023058681396 y[1] (numeric) 1.5903023058681398 absolute error 2.220446049250313e-16 relative error 1.3962414825514452e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0999999999999999 y[1] (analytic) 1.6140961214255773 y[1] (numeric) 1.6140961214255776 absolute error 2.220446049250313e-16 relative error 1.3756591195381875e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2 y[1] (analytic) 1.6343577544766736 y[1] (numeric) 1.6343577544766736 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3 y[1] (analytic) 1.6519988286245875 y[1] (numeric) 1.6519988286245875 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4000000000000001 y[1] (analytic) 1.667967142900241 y[1] (numeric) 1.667967142900241 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5000000000000002 y[1] (analytic) 1.6832372016677029 y[1] (numeric) 1.6832372016677029 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6000000000000003 y[1] (analytic) 1.6988004776987113 y[1] (numeric) 1.6988004776987111 absolute error 2.220446049250313e-16 relative error 1.3070670030998882e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.029187071713790258 Order of pole (three term test) 26.999147387897377 Derivative of radius w.r.t nth term 3.1767869851744355e+53 Derivative of order w.r.t nth term 9.28002321570559e+51 Derivative of radius w.r.t (n-1)th term 4.0243208974710634e+52 Derivative of order w.r.t (n-1)th term -1.3449688900835703e+53 Derivative of radius w.r.t (n-2)th term -3.861650083638572e+45 Derivative of order w.r.t (n-2)th term -8.690268057955787e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.058324372926413875 Guess error in order 0.0025556554656852677 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7000000000000004 y[1] (analytic) 1.7156555057044753 y[1] (numeric) 1.7156555057044751 absolute error 2.220446049250313e-16 relative error 1.2942260505488616e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.12777055101341595 Order of pole (three term test) 26.983399096289723 Derivative of radius w.r.t nth term 1.3796802933386512e+54 Derivative of order w.r.t nth term 1.7925836211086347e+53 Derivative of radius w.r.t (n-1)th term 3.86651553161814e+52 Derivative of order w.r.t (n-1)th term -5.92638406830367e+53 Derivative of radius w.r.t (n-2)th term -3.317747072719302e+47 Derivative of order w.r.t (n-2)th term -8.621509211779392e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.25129888879806833 Guess error in order 0.04897594111880735 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8000000000000005 y[1] (analytic) 1.7347979053069131 y[1] (numeric) 1.7347979053069127 absolute error 4.440892098500626e-16 relative error 2.5598901664081514e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.22126022164742656 Order of pole (three term test) 26.94837920816708 Derivative of radius w.r.t nth term 2.346265453806132e+54 Derivative of order w.r.t nth term 5.473920240788036e+53 Derivative of radius w.r.t (n-1)th term 3.5219687663237804e+52 Derivative of order w.r.t (n-1)th term -1.041767916483293e+54 Derivative of radius w.r.t (n-2)th term -1.819209318639332e+48 Derivative of order w.r.t (n-2)th term -8.466607095450963e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.4196771876097151 Guess error in order 0.14686825705040008 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9000000000000006 y[1] (analytic) 1.7572104331364966 y[1] (numeric) 1.7572104331364964 absolute error 2.220446049250313e-16 relative error 1.2636198871679663e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.30592894547135996 Order of pole (three term test) 26.89548385595721 Derivative of radius w.r.t nth term 3.152334107741935e+54 Derivative of order w.r.t nth term 1.0769487835423414e+54 Derivative of radius w.r.t (n-1)th term 3.0186076106159515e+52 Derivative of order w.r.t (n-1)th term -1.4752988153591231e+54 Derivative of radius w.r.t (n-2)th term -5.241079494544894e+48 Derivative of order w.r.t (n-2)th term -8.227109439713009e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.5479088634792317 Guess error in order 0.2807775590316637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0000000000000004 y[1] (analytic) 1.7838531634528578 y[1] (numeric) 1.7838531634528574 absolute error 4.440892098500626e-16 relative error 2.489494196879275e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3784012476539645 Order of pole (three term test) 26.826821810431806 Derivative of radius w.r.t nth term 3.746634369218252e+54 Derivative of order w.r.t nth term 1.7146755224986245e+54 Derivative of radius w.r.t (n-1)th term 2.3969888619662696e+52 Derivative of order w.r.t (n-1)th term -1.8872639294284142e+54 Derivative of radius w.r.t (n-2)th term -1.1178549945130561e+49 Derivative of order w.r.t (n-2)th term -7.905409225974226e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.6257408093098099 Guess error in order 0.42956251267823203 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1000000000000005 y[1] (analytic) 1.8156538954001427 y[1] (numeric) 1.8156538954001424 absolute error 2.220446049250313e-16 relative error 1.22294565879306e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4357878862067943 Order of pole (three term test) 26.745130410670352 Derivative of radius w.r.t nth term 4.0961333714980975e+54 Derivative of order w.r.t nth term 2.3956146172861302e+54 Derivative of radius w.r.t (n-1)th term 1.7067203212021196e+52 Derivative of order w.r.t (n-1)th term -2.272521227524013e+54 Derivative of radius w.r.t (n-2)th term -1.9958261453589677e+49 Derivative of order w.r.t (n-2)th term -7.504720776430372e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.6494376132288641 Guess error in order 0.5697332452937702 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2000000000000006 y[1] (analytic) 1.8534988827446546 y[1] (numeric) 1.8534988827446541 absolute error 4.440892098500626e-16 relative error 2.395950782513863e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.830019744091102 Order of pole (ratio test) 88.03614940845304 Radius of convergence (three term test) for eq 1 0.475801036944758 Order of pole (three term test) 26.653666434989205 Derivative of radius w.r.t nth term 4.1887676196469605e+54 Derivative of order w.r.t nth term 3.048986257006713e+54 Derivative of radius w.r.t (n-1)th term 1.0020886215966114e+52 Derivative of order w.r.t (n-1)th term -2.6268968315408692e+54 Derivative of radius w.r.t (n-2)th term -3.1614589993900763e+49 Derivative of order w.r.t (n-2)th term -7.029047637619293e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.6220303351676981 Guess error in order 0.6791598802731282 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3000000000000007 y[1] (analytic) 1.8982239787201762 y[1] (numeric) 1.8982239787201758 absolute error 4.440892098500626e-16 relative error 2.3394984724061763e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 16.976204802651484 Order of pole (ratio test) 111.83454007417619 Radius of convergence (three term test) for eq 1 0.49684550181673226 Order of pole (three term test) 26.556076263467528 Derivative of radius w.r.t nth term 4.0343291840886455e+54 Derivative of order w.r.t nth term 3.6046104458106616e+54 Derivative of radius w.r.t (n-1)th term 3.372836341731361e+51 Derivative of order w.r.t (n-1)th term -2.947255708362991e+54 Derivative of radius w.r.t (n-2)th term -4.587839643264269e+49 Derivative of order w.r.t (n-2)th term -6.483142578307371e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.5525679803417933 Guess error in order 0.7405663580265601 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.400000000000001 y[1] (analytic) 1.950606284458755 y[1] (numeric) 1.9506062844587546 absolute error 4.440892098500626e-16 relative error 2.2766727113938648e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 18.32028579346818 Order of pole (ratio test) 122.01667147889145 Radius of convergence (three term test) for eq 1 0.49808230441792023 Order of pole (three term test) 26.456250508280274 Derivative of radius w.r.t nth term 3.663410486504908e+54 Derivative of order w.r.t nth term 3.999294037007942e+54 Derivative of radius w.r.t (n-1)th term -2.3835469719629727e+51 Derivative of order w.r.t (n-1)th term -3.231496747782877e+54 Derivative of radius w.r.t (n-2)th term -6.219335349832814e+49 Derivative of order w.r.t (n-2)th term -5.872460101395008e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.4545006091121747 Guess error in order 0.7442579459228023 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.500000000000001 y[1] (analytic) 2.011356384453067 y[1] (numeric) 2.0113563844530664 absolute error 4.440892098500626e-16 relative error 2.2079091168660322e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.940445944773185 Order of pole (ratio test) 96.51891642771133 Radius of convergence (three term test) for eq 1 0.47946213733156906 Order of pole (three term test) 26.358168907268386 Derivative of radius w.r.t nth term 3.1245037408841375e+54 Derivative of order w.r.t nth term 4.182611084613908e+54 Derivative of radius w.r.t (n-1)th term -6.846433786547486e+51 Derivative of order w.r.t (n-1)th term -3.478475513366887e+54 Derivative of radius w.r.t (n-2)th term -7.975846865872601e+49 Derivative of order w.r.t (n-2)th term -5.2031019443267245e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.3434568596092261 Guess error in order 0.6896518234036747 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.600000000000001 y[1] (analytic) 2.0811112466310533 y[1] (numeric) 2.081111246631053 absolute error 4.440892098500626e-16 relative error 2.133904232985928e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4417273278600762 Order of pole (three term test) 26.26574166434981 Derivative of radius w.r.t nth term 2.4795158249038154e+54 Derivative of order w.r.t nth term 4.121558816910881e+54 Derivative of radius w.r.t (n-1)th term -9.740335164986268e+51 Derivative of order w.r.t (n-1)th term -3.687864213845062e+54 Derivative of radius w.r.t (n-2)th term -9.759307612624461e+49 Derivative of order w.r.t (n-2)th term -4.481756112547558e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.23477071058866236 Guess error in order 0.5853690965352092 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.700000000000001 y[1] (analytic) 2.1604278579829397 y[1] (numeric) 2.1604278579829392 absolute error 4.440892098500626e-16 relative error 2.05556139358748e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.38638224377799313 Order of pole (three term test) 26.182653562028687 Derivative of radius w.r.t nth term 1.798100758185543e+54 Derivative of order w.r.t nth term 3.803671813296171e+54 Derivative of radius w.r.t (n-1)th term -1.0939481129595331e+52 Derivative of order w.r.t (n-1)th term -3.859963823923108e+54 Derivative of radius w.r.t (n-2)th term -1.1461855797718384e+50 Derivative of order w.r.t (n-2)th term -3.715630055163429e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.14114818626137024 Guess error in order 0.44787371492075034 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.800000000000001 y[1] (analytic) 2.249777659331343 y[1] (numeric) 2.2497776593313423 absolute error 8.881784197001252e-16 relative error 3.947849762025377e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.31563331893615987 Order of pole (three term test) 26.11221706074487 Derivative of radius w.r.t nth term 1.1513174247621397e+54 Derivative of order w.r.t nth term 3.2383145442820145e+54 Derivative of radius w.r.t (n-1)th term -1.0477729089182519e+52 Derivative of order w.r.t (n-1)th term -3.99548730699382e+54 Derivative of radius w.r.t (n-2)th term -1.2974955322003528e+50 Derivative of order w.r.t (n-2)th term -2.9123786504921064e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.07083888664833068 Guess error in order 0.29887317606796593 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9000000000000012 y[1] (analytic) 2.349541834850411 y[1] (numeric) 2.34954183485041 absolute error 8.881784197001252e-16 relative error 3.780219643361546e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.23230108970687754 Order of pole (three term test) 26.05724024152934 Derivative of radius w.r.t nth term 6.051802784319782e+53 Derivative of order w.r.t nth term 2.456035026980091e+54 Derivative of radius w.r.t (n-1)th term -8.544130896477818e+51 Derivative of order w.r.t (n-1)th term -4.095335201156767e+54 Derivative of radius w.r.t (n-2)th term -1.419865587421602e+50 Derivative of order w.r.t (n-2)th term -2.0800277210494506e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.026593940964700913 Guess error in order 0.16189138883700743 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.0000000000000013 y[1] (analytic) 2.460007503399556 y[1] (numeric) 2.4600075033995554 absolute error 4.440892098500626e-16 relative error 1.805235184186889e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.13970774909946163 Order of pole (three term test) 26.019914856674813 Derivative of radius w.r.t nth term 2.146801445970588e+53 Derivative of order w.r.t nth term 1.5060354321268721e+54 Derivative of radius w.r.t (n-1)th term -5.464568591288405e+51 Derivative of order w.r.t (n-1)th term -4.160385220710633e+54 Derivative of radius w.r.t (n-2)th term -1.5050169384300445e+50 Derivative of order w.r.t (n-2)th term -1.2268938421838187e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.005564519599354084 Guess error in order 0.058554765475314595 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.1000000000000014 y[1] (analytic) 2.5813648497267225 y[1] (numeric) 2.5813648497267216 absolute error 8.881784197001252e-16 relative error 3.4407318275607287e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.04154470140874687 Order of pole (three term test) 26.0017289514884 Derivative of radius w.r.t nth term 1.8810045099399184e+52 Derivative of order w.r.t nth term 4.519835937483605e+53 Derivative of radius w.r.t (n-1)th term -1.6711140096248736e+51 Derivative of order w.r.t (n-1)th term -4.1913159658688895e+54 Derivative of radius w.r.t (n-2)th term -1.5471000241524857e+50 Derivative of order w.r.t (n-2)th term -3.615012456042729e+155 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.00014365754667083896 Guess error in order 0.005177886645425836 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.2000000000000015 y[1] (analytic) 2.713705224205249 y[1] (numeric) 2.713705224205248 absolute error 8.881784197001252e-16 relative error 3.272936248852313e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.3000000000000016 y[1] (analytic) 2.8570202300911376 y[1] (numeric) 2.8570202300911367 absolute error 8.881784197001252e-16 relative error 3.108757895185757e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.4000000000000017 y[1] (analytic) 3.0112018074205418 y[1] (numeric) 3.011201807420541 absolute error 8.881784197001252e-16 relative error 2.9495811855298976e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.5000000000000018 y[1] (analytic) 3.176043312709207 y[1] (numeric) 3.1760433127092056 absolute error 1.3322676295501878e-15 relative error 4.194740116480798e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.600000000000002 y[1] (analytic) 3.3512415836658564 y[1] (numeric) 3.351241583665855 absolute error 1.3322676295501878e-15 relative error 3.9754449098618753e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.700000000000002 y[1] (analytic) 3.5363999682895955 y[1] (numeric) 3.536399968289594 absolute error 1.3322676295501878e-15 relative error 3.767299065423723e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.800000000000002 y[1] (analytic) 3.7310322880855873 y[1] (numeric) 3.731032288085586 absolute error 1.3322676295501878e-15 relative error 3.570774859827819e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.471121810062579 Order of pole (ratio test) 100.52244763500094 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.900000000000002 y[1] (analytic) 3.9345676957998643 y[1] (numeric) 3.9345676957998625 absolute error 1.7763568394002505e-15 relative error 4.5147446345795614e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 18.94849299871794 Order of pole (ratio test) 126.75583215151322 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.000000000000002 y[1] (analytic) 4.1463563791363915 y[1] (numeric) 4.146356379136391 absolute error 8.881784197001252e-16 relative error 2.1420696594466784e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 16.41013193456165 Order of pole (ratio test) 107.55365267869504 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.100000000000001 y[1] (analytic) 4.365676053466734 y[1] (numeric) 4.365676053466734 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.200000000000001 y[1] (analytic) 4.591739178659303 y[1] (numeric) 4.591739178659303 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.300000000000001 y[1] (analytic) 4.823700827920026 y[1] (numeric) 4.823700827920027 absolute error 8.881784197001252e-16 relative error 1.841280069773951e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.4 y[1] (analytic) 5.0606671300215815 y[1] (numeric) 5.060667130021583 absolute error 1.7763568394002505e-15 relative error 3.510123850790943e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.5 y[1] (analytic) 5.301704200569221 y[1] (numeric) 5.301704200569223 absolute error 2.6645352591003757e-15 relative error 5.025808981976581e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.6 y[1] (analytic) 5.545847473064945 y[1] (numeric) 5.545847473064948 absolute error 3.552713678800501e-15 relative error 6.406078955570469e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.699999999999999 y[1] (analytic) 5.792111336537108 y[1] (numeric) 5.792111336537112 absolute error 4.440892098500626e-15 relative error 7.667138700333881e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.799999999999999 y[1] (analytic) 6.039498983439444 y[1] (numeric) 6.03949898343945 absolute error 6.217248937900877e-15 relative error 1.0294312417220088e-13% Correct digits 15 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.08716339061148899 Order of pole (three term test) 26.992343927897068 Derivative of radius w.r.t nth term -9.454705701202074e+53 Derivative of order w.r.t nth term -8.304622852849214e+52 Derivative of radius w.r.t (n-1)th term -3.9559310813642345e+52 Derivative of order w.r.t (n-1)th term 4.027865595364798e+53 Derivative of radius w.r.t (n-2)th term 1.0390936746768426e+47 Derivative of order w.r.t (n-2)th term 8.660630347070782e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.17299212281646206 Guess error in order 0.02279236998865816 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.899999999999999 y[1] (analytic) 6.287012369422572 y[1] (numeric) 6.287012369422579 absolute error 6.217248937900877e-15 relative error 9.88903563819757e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.18323956462596255 Order of pole (three term test) 26.965213136052377 Derivative of radius w.r.t nth term -1.9602598919702547e+54 Derivative of order w.r.t nth term -3.721428519170485e+53 Derivative of radius w.r.t (n-1)th term -3.6864861245387417e+52 Derivative of order w.r.t (n-1)th term 8.564915990674525e+53 Derivative of radius w.r.t (n-2)th term 1.0063952928824641e+48 Derivative of order w.r.t (n-2)th term 8.54141859285367e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.35373046964299504 Guess error in order 0.10073021413292678 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.999999999999998 y[1] (analytic) 6.533662185463222 y[1] (numeric) 6.533662185463229 absolute error 7.105427357601002e-15 relative error 1.0875106725612326e-13% Correct digits 15 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2720105554446835 Order of pole (three term test) 26.919535764538224 Derivative of radius w.r.t nth term -2.840225752927465e+54 Derivative of order w.r.t nth term -8.40175460744674e+53 Derivative of radius w.r.t (n-1)th term -3.2449075252424836e+52 Derivative of order w.r.t (n-1)th term 1.2972759680843017e+54 Derivative of radius w.r.t (n-2)th term 3.5403810911957696e+48 Derivative of order w.r.t (n-2)th term 8.33686380747439e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.5002468681265899 Guess error in order 0.22196922681998058 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = (0.1 * x + 1.0) - sin(x); Iterations 50 Total Elapsed Time 0.0 Seconds Elapsed Time(since restart) 0.0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 104.08163265306118%