##############ECHO OF PROBLEM################# ##############temp/sing2postode.ode################# diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=16; ELIMINATED in preodein.rb max_terms=20 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(-2.0) x_end=c(-1.5) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=c(0.001) $glob_min_h=c(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 # ELIMINATED in preodein.rb $glob_type_given_pole=2 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(0.0) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(1.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(1.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=c(0.0) #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=8 $glob_max_minutes=(3.0) $glob_subiter_method=3 $glob_max_iter=100000 $glob_upper_ratio_limit=c(1.000001) $glob_lower_ratio_limit=c(0.999999) $glob_look_poles=true $glob_h=c(0.001) $glob_display_interval=c(0.01) #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(arctan(c(x))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] -2.0 y[1] (closed_form) -1.1071487177940904 y[1] (numeric) -1.1071487177940904 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.2360679774997525 Order of pole (six term test) -9.50350909079134e-14 TOP MAIN SOLVE Loop x[1] -1.990000000000001 y[1] (closed_form) -1.1051406883644945 y[1] (numeric) -1.1051406883644943 absolute error 2.220446049250313e-16 relative error 2.009197627621843e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 2.2271281956816056 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.2271281956815936 Order of pole (six term test) -3.108624468950438e-14 TOP MAIN SOLVE Loop x[1] -1.9800000000000022 y[1] (closed_form) -1.1031164815829975 y[1] (numeric) -1.103116481582997 absolute error 4.440892098500626e-16 relative error 4.0257689669615343e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 2.218197466412765 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.2181974664127604 Order of pole (six term test) -1.1546319456101628e-14 TOP MAIN SOLVE Loop x[1] -1.9700000000000033 y[1] (closed_form) -1.101075917953987 y[1] (numeric) -1.1010759179539864 absolute error 6.661338147750939e-16 relative error 6.049844555795026e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 2.2092758994747608 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.2092758994747386 Order of pole (six term test) -5.595524044110789e-14 TOP MAIN SOLVE Loop x[1] -1.9600000000000044 y[1] (closed_form) -1.0990188156141476 y[1] (numeric) -1.0990188156141465 absolute error 1.1102230246251565e-15 relative error 1.0101947381171521e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.2003636063160146 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.200363606315985 Order of pole (six term test) -7.37188088351104e-14 TOP MAIN SOLVE Loop x[1] -1.9500000000000055 y[1] (closed_form) -1.0969449903001374 y[1] (numeric) -1.096944990300136 absolute error 1.3322676295501878e-15 relative error 1.2145254696734275e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.1914607000811173 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.1914607000810604 Order of pole (six term test) -1.438849039914203e-13 TOP MAIN SOLVE Loop x[1] -1.9400000000000066 y[1] (closed_form) -1.0948542553159395 y[1] (numeric) -1.0948542553159377 absolute error 1.7763568394002505e-15 relative error 1.6224596386006204e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.1825672956406237 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.182567295640563 Order of pole (six term test) -1.5010215292932116e-13 TOP MAIN SOLVE Loop x[1] -1.9300000000000077 y[1] (closed_form) -1.092746421499887 y[1] (numeric) -1.092746421499885 absolute error 1.9984014443252818e-15 relative error 1.8287879099913285e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.173683509621405 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.173683509621416 Order of pole (six term test) 2.4868995751603507e-14 TOP MAIN SOLVE Loop x[1] -1.9200000000000088 y[1] (closed_form) -1.0906212971913716 y[1] (numeric) -1.0906212971913694 absolute error 2.220446049250313e-15 relative error 2.035945983237746e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.164809460437577 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.164809460437587 Order of pole (six term test) 2.5757174171303632e-14 TOP MAIN SOLVE Loop x[1] -1.91000000000001 y[1] (closed_form) -1.0884786881972388 y[1] (numeric) -1.0884786881972366 absolute error 2.220446049250313e-15 relative error 2.0399536282404044e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.155945268322004 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.1559452683220117 Order of pole (six term test) 2.042810365310288e-14 TOP MAIN SOLVE Loop x[1] -1.900000000000011 y[1] (closed_form) -1.0863183977578759 y[1] (numeric) -1.0863183977578736 absolute error 2.220446049250313e-15 relative error 2.044010350771227e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.147091055358399 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.147091055358386 Order of pole (six term test) -3.108624468950438e-14 TOP MAIN SOLVE Loop x[1] -1.8900000000000121 y[1] (closed_form) -1.0841402265129996 y[1] (numeric) -1.0841402265129971 absolute error 2.4424906541753444e-15 relative error 2.252928721251593e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.138246945514022 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.1382469455140067 Order of pole (six term test) -3.375077994860476e-14 TOP MAIN SOLVE Loop x[1] -1.8800000000000132 y[1] (closed_form) -1.0819439724671518 y[1] (numeric) -1.081943972467149 absolute error 2.886579864025407e-15 relative error 2.6679568789899097e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.129413064672998 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.129413064672962 Order of pole (six term test) -8.260059303211165e-14 TOP MAIN SOLVE Loop x[1] -1.8700000000000143 y[1] (closed_form) -1.0797294309549097 y[1] (numeric) -1.0797294309549066 absolute error 3.1086244689504383e-15 relative error 2.879077276055335e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.120589540670248 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.1205895406701973 Order of pole (six term test) -1.1546319456101628e-13 TOP MAIN SOLVE Loop x[1] -1.8600000000000154 y[1] (closed_form) -1.0774963946058211 y[1] (numeric) -1.0774963946058174 absolute error 3.774758283725532e-15 relative error 3.503267669964173e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.111776503326064 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.1117765033260323 Order of pole (six term test) -7.37188088351104e-14 TOP MAIN SOLVE Loop x[1] -1.8500000000000165 y[1] (closed_form) -1.0752446533090718 y[1] (numeric) -1.0752446533090676 absolute error 4.218847493575595e-15 relative error 3.923616342189721e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.102974084481324 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.1029740844813163 Order of pole (six term test) -1.2434497875801753e-14 TOP MAIN SOLVE Loop x[1] -1.8400000000000176 y[1] (closed_form) -1.0729739941778995 y[1] (numeric) -1.0729739941778949 absolute error 4.6629367034256575e-15 relative error 4.345805889730204e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.0941824180333635 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.094182418033342 Order of pole (six term test) -4.440892098500626e-14 TOP MAIN SOLVE Loop x[1] -1.8300000000000187 y[1] (closed_form) -1.0706842015137612 y[1] (numeric) -1.0706842015137563 absolute error 4.884981308350689e-15 relative error 4.562485653047066e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.085401639972518 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.0854016399725115 Order of pole (six term test) -1.0658141036401503e-14 TOP MAIN SOLVE Loop x[1] -1.8200000000000198 y[1] (closed_form) -1.0683750567702706 y[1] (numeric) -1.0683750567702648 absolute error 5.773159728050814e-15 relative error 5.403682622002845e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.0766318884193393 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.076631888419327 Order of pole (six term test) -2.842170943040401e-14 TOP MAIN SOLVE Loop x[1] -1.810000000000021 y[1] (closed_form) -1.066046338516914 y[1] (numeric) -1.0660463385169083 absolute error 5.773159728050814e-15 relative error 5.415486662692774e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.067873303662503 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.0678733036624943 Order of pole (six term test) -1.9539925233402755e-14 TOP MAIN SOLVE Loop x[1] -1.800000000000022 y[1] (closed_form) -1.0636978224025648 y[1] (numeric) -1.063697822402559 absolute error 5.773159728050814e-15 relative error 5.427443402122446e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.0591260281974195 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.0591260281974044 Order of pole (six term test) -2.6645352591003757e-14 TOP MAIN SOLVE Loop x[1] -1.7900000000000231 y[1] (closed_form) -1.0613292811188053 y[1] (numeric) -1.0613292811187998 absolute error 5.551115123125783e-15 relative error 5.230342007782964e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.050390206765552 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.0503902067655395 Order of pole (six term test) -2.6645352591003757e-14 TOP MAIN SOLVE Loop x[1] -1.7800000000000242 y[1] (closed_form) -1.0589404843630783 y[1] (numeric) -1.0589404843630723 absolute error 5.995204332975845e-15 relative error 5.66151206937922e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.0416659863944657 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.0416659863944417 Order of pole (six term test) -4.618527782440651e-14 TOP MAIN SOLVE Loop x[1] -1.7700000000000253 y[1] (closed_form) -1.0565311988016812 y[1] (numeric) -1.0565311988016748 absolute error 6.439293542825908e-15 relative error 6.094750017916519e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.0329535164386052 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.032953516438597 Order of pole (six term test) -1.5987211554602254e-14 TOP MAIN SOLVE Loop x[1] -1.7600000000000264 y[1] (closed_form) -1.0541011880326259 y[1] (numeric) -1.0541011880326192 absolute error 6.661338147750939e-15 relative error 6.319448477411983e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.024252948620822 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.0242529486208123 Order of pole (six term test) -1.9539925233402755e-14 TOP MAIN SOLVE Loop x[1] -1.7500000000000275 y[1] (closed_form) -1.0516502125483804 y[1] (numeric) -1.0516502125483738 absolute error 6.661338147750939e-15 relative error 6.33417658102217e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.0155644370746613 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.015564437074647 Order of pole (six term test) -2.042810365310288e-14 TOP MAIN SOLVE Loop x[1] -1.7400000000000286 y[1] (closed_form) -1.0491780296985171 y[1] (numeric) -1.0491780296985107 absolute error 6.439293542825908e-15 relative error 6.137465101777101e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.0068881383874135 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.006888138387405 Order of pole (six term test) -1.4210854715202004e-14 TOP MAIN SOLVE Loop x[1] -1.7300000000000297 y[1] (closed_form) -1.0466843936522883 y[1] (numeric) -1.0466843936522816 absolute error 6.661338147750939e-15 relative error 6.364228021502207e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9982242116439544 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9982242116439393 Order of pole (six term test) -2.842170943040401e-14 TOP MAIN SOLVE Loop x[1] -1.7200000000000308 y[1] (closed_form) -1.0441690553611538 y[1] (numeric) -1.0441690553611467 absolute error 7.105427357601002e-15 relative error 6.80486298757762e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9895728184713688 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9895728184713717 Order of pole (six term test) 1.2434497875801753e-14 TOP MAIN SOLVE Loop x[1] -1.710000000000032 y[1] (closed_form) -1.0416317625212894 y[1] (numeric) -1.041631762521282 absolute error 7.327471962526033e-15 relative error 7.034608799552875e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.980934123084387 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.980934123084388 Order of pole (six term test) -7.993605777301127e-15 TOP MAIN SOLVE Loop x[1] -1.700000000000033 y[1] (closed_form) -1.0390722595360995 y[1] (numeric) -1.039072259536092 absolute error 7.549516567451064e-15 relative error 7.265631911703229e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9723082923316304 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.972308292331623 Order of pole (six term test) -9.769962616701378e-15 TOP MAIN SOLVE Loop x[1] -1.6900000000000341 y[1] (closed_form) -1.0364902874787651 y[1] (numeric) -1.0364902874787572 absolute error 7.993605777301127e-15 relative error 7.712185896835906e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9636954957426866 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9636954957426804 Order of pole (six term test) 3.552713678800501e-15 TOP MAIN SOLVE Loop x[1] -1.6800000000000352 y[1] (closed_form) -1.0338855840548602 y[1] (numeric) -1.0338855840548522 absolute error 7.993605777301127e-15 relative error 7.731615471366287e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9550959055760202 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9550959055760113 Order of pole (six term test) -2.6645352591003757e-15 TOP MAIN SOLVE Loop x[1] -1.6700000000000363 y[1] (closed_form) -1.0312578835650676 y[1] (numeric) -1.031257883565059 absolute error 8.659739592076221e-15 relative error 8.397259046533952e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.946509696867735 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9465096968677302 Order of pole (six term test) 1.7763568394002505e-15 TOP MAIN SOLVE Loop x[1] -1.6600000000000374 y[1] (closed_form) -1.0286069168680279 y[1] (numeric) -1.0286069168680192 absolute error 8.659739592076221e-15 relative error 8.418900796860266e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9379370474811932 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9379370474811886 Order of pole (six term test) 1.7763568394002505e-15 TOP MAIN SOLVE Loop x[1] -1.6500000000000385 y[1] (closed_form) -1.0259324113433632 y[1] (numeric) -1.0259324113433541 absolute error 9.103828801926284e-15 relative error 8.873712050880296e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9293781381575068 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9293781381575021 Order of pole (six term test) -8.881784197001252e-15 TOP MAIN SOLVE Loop x[1] -1.6400000000000396 y[1] (closed_form) -1.0232340908549098 y[1] (numeric) -1.0232340908549005 absolute error 9.325873406851315e-15 relative error 9.114115225636753e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.920833152566909 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9208331525669062 Order of pole (six term test) 8.881784197001252e-15 TOP MAIN SOLVE Loop x[1] -1.6300000000000407 y[1] (closed_form) -1.0205116757142045 y[1] (numeric) -1.0205116757141948 absolute error 9.769962616701378e-15 relative error 9.573592198113632e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9123022773610172 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9123022773610172 Order of pole (six term test) 8.881784197001252e-15 TOP MAIN SOLVE Loop x[1] -1.6200000000000419 y[1] (closed_form) -1.0177648826442676 y[1] (numeric) -1.0177648826442576 absolute error 9.992007221626409e-15 relative error 9.817598732298613e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9037857022259979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9037857022259994 Order of pole (six term test) 2.7533531010703882e-14 TOP MAIN SOLVE Loop x[1] -1.610000000000043 y[1] (closed_form) -1.0149934247437293 y[1] (numeric) -1.014993424743719 absolute error 1.0436096431476471e-14 relative error 1.028193501264447e-12% Desired digits 8 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8952836199366412 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.89528361993664 Order of pole (six term test) 1.1546319456101628e-14 TOP MAIN SOLVE Loop x[1] -1.600000000000044 y[1] (closed_form) -1.0121970114513466 y[1] (numeric) -1.0121970114513361 absolute error 1.0436096431476471e-14 relative error 1.0310341083217183e-12% Desired digits 8 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.886796226411358 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.88679622641136 Order of pole (six term test) 1.687538997430238e-14 TOP MAIN SOLVE Loop x[1] -1.5900000000000452 y[1] (closed_form) -1.009375348510965 y[1] (numeric) -1.0093753485109545 absolute error 1.0658141036401503e-14 relative error 1.0559145368593e-12% Desired digits 8 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8783237207681065 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8783237207681063 Order of pole (six term test) 6.217248937900877e-15 TOP MAIN SOLVE Loop x[1] -1.5800000000000463 y[1] (closed_form) -1.0065281379369782 y[1] (numeric) -1.006528137936967 absolute error 1.1102230246251565e-14 relative error 1.1030223426249322e-12% Desired digits 8 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8698663053812554 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8698663053812545 Order of pole (six term test) 1.4210854715202004e-14 TOP MAIN SOLVE Loop x[1] -1.5700000000000474 y[1] (closed_form) -1.0036550779803408 y[1] (numeric) -1.0036550779803295 absolute error 1.1324274851176597e-14 relative error 1.128303448029624e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8614241859393976 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8614241859393972 Order of pole (six term test) -1.4210854715202004e-14 TOP MAIN SOLVE Loop x[1] -1.5600000000000485 y[1] (closed_form) -1.0007558630952005 y[1] (numeric) -1.0007558630951883 absolute error 1.2212453270876722e-14 relative error 1.2203229300206427e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8529975715041158 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8529975715041171 Order of pole (six term test) 9.769962616701378e-15 TOP MAIN SOLVE Loop x[1] -1.5500000000000496 y[1] (closed_form) -0.997830183906205 y[1] (numeric) -0.9978301839061924 absolute error 1.2656542480726785e-14 relative error 1.2684064568161516e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8445866745697133 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8445866745697155 Order of pole (six term test) 1.509903313490213e-14 TOP MAIN SOLVE Loop x[1] -1.5400000000000507 y[1] (closed_form) -0.9948777271765586 y[1] (numeric) -0.9948777271765455 absolute error 1.3100631690576847e-14 relative error 1.3168082200167608e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.836191711123911 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8361917111239154 Order of pole (six term test) 4.085620730620576e-14 TOP MAIN SOLVE Loop x[1] -1.5300000000000518 y[1] (closed_form) -0.9918981757768925 y[1] (numeric) -0.9918981757768793 absolute error 1.3211653993039363e-14 relative error 1.331956678183372e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8278129007095225 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8278129007095172 Order of pole (six term test) -2.930988785010413e-14 TOP MAIN SOLVE Loop x[1] -1.5200000000000529 y[1] (closed_form) -0.988891208655027 y[1] (numeric) -0.9888912086550136 absolute error 1.3433698597964394e-14 relative error 1.358460716445778e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8194504664871096 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8194504664871145 Order of pole (six term test) 2.842170943040401e-14 TOP MAIN SOLVE Loop x[1] -1.510000000000054 y[1] (closed_form) -0.9858565008067001 y[1] (numeric) -0.9858565008066863 absolute error 1.3766765505351941e-14 relative error 1.3964269134592068e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8111046352986244 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8111046352986293 Order of pole (six term test) 3.6415315207705135e-14 TOP MAIN SOLVE Loop x[1] -1.500000000000055 y[1] (closed_form) -0.982793723247346 y[1] (numeric) -0.982793723247332 absolute error 1.3988810110276972e-14 relative error 1.423371942593931e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8027756377320405 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8027756377320499 Order of pole (six term test) 6.661338147750939e-14 Finished! diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; Iterations 501 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.39999999998895%