##############ECHO OF PROBLEM################# ##############temp/ln_sqrtpostode.ode################# diff ( y , x , 1 ) = ln ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(10.0) x_end=c(11.0) $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]=c(-2.0) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(0.5) # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb #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(c(5.0) * ln(c(0.1) * c(x) + c(0.2)) * ( c(0.1) * c(x) + c(0.2)) - c(0.5) * c(x) - c(1.0)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 10.0 y[1] (closed_form) -4.906070659236272 y[1] (numeric) -4.906070659236272 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 12.0 Order of pole (given) 0.5 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] 10.009999999999994 y[1] (closed_form) -4.905156968697433 y[1] (numeric) -4.90515696869454 absolute error 2.892797112963308e-12 relative error 5.897460838509091e-11% Desired digits 8 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 12.009999999999994 Order of pole (given) 0.5 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] 10.019999999999989 y[1] (closed_form) -4.904239114960776 y[1] (numeric) -4.904239114954997 absolute error 5.778488798569015e-12 relative error 1.17826408197375e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 Radius of convergence (given) for eq 1 12.019999999999989 Order of pole (given) 0.5 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] 10.029999999999983 y[1] (closed_form) -4.903317101489863 y[1] (numeric) -4.903317101481201 absolute error 8.662404127335321e-12 relative error 1.7666416321928816e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 Radius of convergence (given) for eq 1 12.029999999999983 Order of pole (given) 0.5 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] 10.039999999999978 y[1] (closed_form) -4.902390931742493 y[1] (numeric) -4.902390931730955 absolute error 1.1538325850324327e-11 relative error 2.353611943840467e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 Radius of convergence (given) for eq 1 12.039999999999978 Order of pole (given) 0.5 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] 10.049999999999972 y[1] (closed_form) -4.901460609170727 y[1] (numeric) -4.901460609156316 absolute error 1.4411583038054232e-11 relative error 2.94026295163729e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 Radius of convergence (given) for eq 1 12.049999999999972 Order of pole (given) 0.5 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] 10.059999999999967 y[1] (closed_form) -4.900526137220892 y[1] (numeric) -4.900526137203611 absolute error 1.7280399333685637e-11 relative error 3.5262334797964005e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 Radius of convergence (given) for eq 1 12.059999999999967 Order of pole (given) 0.5 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] 10.069999999999961 y[1] (closed_form) -4.899587519333599 y[1] (numeric) -4.899587519313456 absolute error 2.014299838037914e-11 relative error 4.1111620725001e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 Radius of convergence (given) for eq 1 12.069999999999961 Order of pole (given) 0.5 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] 10.079999999999956 y[1] (closed_form) -4.89864475894376 y[1] (numeric) -4.898644758920759 absolute error 2.3001156534974143e-11 relative error 4.695412234777691e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 Radius of convergence (given) for eq 1 12.079999999999956 Order of pole (given) 0.5 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] 10.08999999999995 y[1] (closed_form) -4.897697859480601 y[1] (numeric) -4.8976978594547464 absolute error 2.5854873797470646e-11 relative error 5.278985053645703e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 Radius of convergence (given) for eq 1 12.08999999999995 Order of pole (given) 0.5 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] 10.099999999999945 y[1] (closed_form) -4.896746824367675 y[1] (numeric) -4.89674682433897 absolute error 2.8705038346288347e-11 relative error 5.862062993218988e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 Radius of convergence (given) for eq 1 12.099999999999945 Order of pole (given) 0.5 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] 10.109999999999939 y[1] (closed_form) -4.895791657022873 y[1] (numeric) -4.895791656991324 absolute error 3.154898564616815e-11 relative error 6.444102988106537e-10% Desired digits 8 Estimated correct digits 12 Correct digits 12 h 0.001 Radius of convergence (given) for eq 1 12.109999999999939 Order of pole (given) 0.5 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] 10.119999999999933 y[1] (closed_form) -4.894832360858443 y[1] (numeric) -4.894832360824056 absolute error 3.438671569711005e-11 relative error 7.025105899863626e-10% Desired digits 8 Estimated correct digits 12 Correct digits 12 h 0.001 Radius of convergence (given) for eq 1 12.119999999999933 Order of pole (given) 0.5 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] 10.129999999999928 y[1] (closed_form) -4.893868939281004 y[1] (numeric) -4.893868939243782 absolute error 3.722266939121255e-11 relative error 7.605980023788953e-10% Desired digits 8 Estimated correct digits 12 Correct digits 12 h 0.001 Radius of convergence (given) for eq 1 12.129999999999928 Order of pole (given) 0.5 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] 10.139999999999922 y[1] (closed_form) -4.892901395691557 y[1] (numeric) -4.892901395651504 absolute error 4.005329401479685e-11 relative error 8.186000651896595e-10% Desired digits 8 Estimated correct digits 12 Correct digits 12 h 0.001 Radius of convergence (given) for eq 1 12.139999999999922 Order of pole (given) 0.5 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] 10.149999999999917 y[1] (closed_form) -4.891929733485499 y[1] (numeric) -4.891929733442621 absolute error 4.2878589567862946e-11 relative error 8.765168737882087e-10% Desired digits 8 Estimated correct digits 12 Correct digits 12 h 0.001 Radius of convergence (given) for eq 1 12.149999999999917 Order of pole (given) 0.5 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] 10.159999999999911 y[1] (closed_form) -4.890953956052639 y[1] (numeric) -4.89095395600694 absolute error 4.5699444228830544e-11 relative error 9.343666826443275e-10% Desired digits 8 Estimated correct digits 12 Correct digits 12 h 0.001 Radius of convergence (given) for eq 1 12.159999999999911 Order of pole (given) 0.5 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] 10.169999999999906 y[1] (closed_form) -4.889974066777211 y[1] (numeric) -4.889974066728695 absolute error 4.851585799769964e-11 relative error 9.921495970156449e-10% Desired digits 8 Estimated correct digits 12 Correct digits 12 h 0.001 Radius of convergence (given) for eq 1 12.169999999999906 Order of pole (given) 0.5 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] 10.1799999999999 y[1] (closed_form) -4.8889900690378845 y[1] (numeric) -4.8889900689865575 absolute error 5.132694269605054e-11 relative error 1.0498475548376658e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.1799999999999 Order of pole (given) 0.5 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] 10.189999999999895 y[1] (closed_form) -4.888001966207786 y[1] (numeric) -4.8880019661536505 absolute error 5.413536285914233e-11 relative error 1.1075151612744068e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.189999999999895 Order of pole (given) 0.5 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] 10.19999999999989 y[1] (closed_form) -4.887009761654504 y[1] (numeric) -4.8870097615975645 absolute error 5.693934213013563e-11 relative error 1.1651161938923308e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.19999999999989 Order of pole (given) 0.5 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] 10.209999999999884 y[1] (closed_form) -4.8860134587401065 y[1] (numeric) -4.886013458680369 absolute error 5.973710415219102e-11 relative error 1.2226144004031185e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.209999999999884 Order of pole (given) 0.5 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] 10.219999999999878 y[1] (closed_form) -4.885013060821157 y[1] (numeric) -4.885013060758626 absolute error 6.253042528214792e-11 relative error 1.2800462251299842e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.219999999999878 Order of pole (given) 0.5 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] 10.229999999999873 y[1] (closed_form) -4.884008571248722 y[1] (numeric) -4.884008571183404 absolute error 6.531752916316691e-11 relative error 1.3373753999466634e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.229999999999873 Order of pole (given) 0.5 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] 10.239999999999867 y[1] (closed_form) -4.882999993368392 y[1] (numeric) -4.88299999330029 absolute error 6.81019685089268e-11 relative error 1.3946747614461636e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.239999999999867 Order of pole (given) 0.5 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] 10.249999999999861 y[1] (closed_form) -4.881987330520286 y[1] (numeric) -4.881987330449405 absolute error 7.08810787841685e-11 relative error 1.4518898552039975e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.249999999999861 Order of pole (given) 0.5 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] 10.259999999999856 y[1] (closed_form) -4.880970586039075 y[1] (numeric) -4.880970585965419 absolute error 7.365574816731169e-11 relative error 1.5090389681508733e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.259999999999856 Order of pole (given) 0.5 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] 10.26999999999985 y[1] (closed_form) -4.879949763253984 y[1] (numeric) -4.879949763177559 absolute error 7.642508847993668e-11 relative error 1.5661040008120062e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.26999999999985 Order of pole (given) 0.5 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] 10.279999999999845 y[1] (closed_form) -4.878924865488819 y[1] (numeric) -4.878924865409626 absolute error 7.919265243572227e-11 relative error 1.6231578599599518e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.279999999999845 Order of pole (given) 0.5 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] 10.28999999999984 y[1] (closed_form) -4.877895896061965 y[1] (numeric) -4.8778958959800125 absolute error 8.195222278573056e-11 relative error 1.680073222798634e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.28999999999984 Order of pole (given) 0.5 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] 10.299999999999834 y[1] (closed_form) -4.876862858286412 y[1] (numeric) -4.876862858201702 absolute error 8.471001677889944e-11 relative error 1.7369776276354855e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.299999999999834 Order of pole (given) 0.5 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] 10.309999999999828 y[1] (closed_form) -4.87582575546976 y[1] (numeric) -4.875825755382298 absolute error 8.746248170155013e-11 relative error 1.7937983448943733e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.309999999999828 Order of pole (given) 0.5 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] 10.319999999999823 y[1] (closed_form) -4.874784590914238 y[1] (numeric) -4.874784590824029 absolute error 9.020961755368262e-11 relative error 1.8505354620554488e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.319999999999823 Order of pole (given) 0.5 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] 10.329999999999817 y[1] (closed_form) -4.873739367916712 y[1] (numeric) -4.8737393678237595 absolute error 9.29523125137166e-11 relative error 1.9072072898606645e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.329999999999817 Order of pole (given) 0.5 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] 10.339999999999812 y[1] (closed_form) -4.8726900897687 y[1] (numeric) -4.87269008967301 absolute error 9.569056658165209e-11 relative error 1.9638139265736554e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.339999999999812 Order of pole (given) 0.5 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] 10.349999999999806 y[1] (closed_form) -4.871636759756388 y[1] (numeric) -4.871636759657964 absolute error 9.842437975748908e-11 relative error 2.0203554700660997e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.349999999999806 Order of pole (given) 0.5 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] 10.3599999999998 y[1] (closed_form) -4.8705793811606375 y[1] (numeric) -4.870579381059483 absolute error 1.0115464021964726e-10 relative error 2.0768502533992694e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.3599999999998 Order of pole (given) 0.5 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] 10.369999999999795 y[1] (closed_form) -4.869517957257003 y[1] (numeric) -4.869517957153121 absolute error 1.0388134796812665e-10 relative error 2.1332983855889292e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.369999999999795 Order of pole (given) 0.5 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] 10.37999999999979 y[1] (closed_form) -4.86845249131574 y[1] (numeric) -4.868452491209139 absolute error 1.0660095028924843e-10 relative error 2.1896270011754525e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.37999999999979 Order of pole (given) 0.5 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] 10.389999999999784 y[1] (closed_form) -4.867382986601825 y[1] (numeric) -4.8673829864925064 absolute error 1.0931877625353081e-10 relative error 2.24594564583158e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.389999999999784 Order of pole (given) 0.5 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] 10.399999999999778 y[1] (closed_form) -4.866309446374962 y[1] (numeric) -4.866309446262932 absolute error 1.120303849688753e-10 relative error 2.3021631937592784e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.399999999999778 Order of pole (given) 0.5 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] 10.409999999999773 y[1] (closed_form) -4.865231873889598 y[1] (numeric) -4.865231873774859 absolute error 1.1473844097054098e-10 relative error 2.358334483219836e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.409999999999773 Order of pole (given) 0.5 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] 10.419999999999767 y[1] (closed_form) -4.864150272394933 y[1] (numeric) -4.864150272277492 absolute error 1.1744116790168846e-10 relative error 2.4144231021848067e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.419999999999767 Order of pole (given) 0.5 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] 10.429999999999762 y[1] (closed_form) -4.863064645134939 y[1] (numeric) -4.863064645014797 absolute error 1.2014211847599654e-10 relative error 2.4705021882896e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.429999999999762 Order of pole (given) 0.5 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] 10.439999999999756 y[1] (closed_form) -4.861974995348364 y[1] (numeric) -4.861974995225528 absolute error 1.2283596362294702e-10 relative error 2.5264622656527204e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.439999999999756 Order of pole (given) 0.5 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] 10.44999999999975 y[1] (closed_form) -4.860881326268752 y[1] (numeric) -4.860881326143224 absolute error 1.255271442346384e-10 relative error 2.582394751261989e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.44999999999975 Order of pole (given) 0.5 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] 10.459999999999745 y[1] (closed_form) -4.85978364112445 y[1] (numeric) -4.859783640996236 absolute error 1.2821388395423128e-10 relative error 2.6382632113343494e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.459999999999745 Order of pole (given) 0.5 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] 10.46999999999974 y[1] (closed_form) -4.858681943138626 y[1] (numeric) -4.8586819430077295 absolute error 1.3089618278172566e-10 relative error 2.6940677392265967e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.46999999999974 Order of pole (given) 0.5 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] 10.479999999999734 y[1] (closed_form) -4.857576235529278 y[1] (numeric) -4.857576235395703 absolute error 1.3357492889554123e-10 relative error 2.7498267123127716e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.479999999999734 Order of pole (given) 0.5 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] 10.489999999999728 y[1] (closed_form) -4.856466521509244 y[1] (numeric) -4.856466521372996 absolute error 1.362483459388386e-10 relative error 2.805503658583787e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.489999999999728 Order of pole (given) 0.5 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] 10.499999999999723 y[1] (closed_form) -4.85535280428622 y[1] (numeric) -4.8553528041473015 absolute error 1.389182102684572e-10 relative error 2.8611352432684737e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.499999999999723 Order of pole (given) 0.5 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] 10.509999999999717 y[1] (closed_form) -4.85423508706277 y[1] (numeric) -4.854235086921187 absolute error 1.4158363370597726e-10 relative error 2.916703273875587e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.509999999999717 Order of pole (given) 0.5 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] 10.519999999999712 y[1] (closed_form) -4.8531133730363365 y[1] (numeric) -4.853113372892092 absolute error 1.4424461625139884e-10 relative error 2.9722078419353432e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.519999999999712 Order of pole (given) 0.5 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] 10.529999999999706 y[1] (closed_form) -4.851987665399254 y[1] (numeric) -4.851987665252354 absolute error 1.469002697263022e-10 relative error 3.0276307331505605e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.529999999999706 Order of pole (given) 0.5 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] 10.5399999999997 y[1] (closed_form) -4.850857967338763 y[1] (numeric) -4.850857967189212 absolute error 1.4955148230910709e-10 relative error 3.0829903352365677e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.5399999999997 Order of pole (given) 0.5 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] 10.549999999999695 y[1] (closed_form) -4.849724282037021 y[1] (numeric) -4.849724281884822 absolute error 1.5219914217823316e-10 relative error 3.138305052556621e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.549999999999695 Order of pole (given) 0.5 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] 10.55999999999969 y[1] (closed_form) -4.848586612671112 y[1] (numeric) -4.848586612516269 absolute error 1.5484324933368043e-10 relative error 3.193574987997924e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.55999999999969 Order of pole (given) 0.5 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] 10.569999999999684 y[1] (closed_form) -4.847444962413062 y[1] (numeric) -4.8474449622555795 absolute error 1.574829155970292e-10 relative error 3.2487819215720207e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.569999999999684 Order of pole (given) 0.5 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] 10.579999999999679 y[1] (closed_form) -4.846299334429852 y[1] (numeric) -4.846299334269734 absolute error 1.6011814096827948e-10 relative error 3.303925942641278e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.579999999999679 Order of pole (given) 0.5 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] 10.589999999999673 y[1] (closed_form) -4.845149731883425 y[1] (numeric) -4.845149731720674 absolute error 1.6275070180427065e-10 relative error 3.3590438027805916e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.589999999999673 Order of pole (given) 0.5 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] 10.599999999999667 y[1] (closed_form) -4.843996157930703 y[1] (numeric) -4.843996157765325 absolute error 1.6537793356974362e-10 relative error 3.4140806098490196e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.599999999999667 Order of pole (given) 0.5 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] 10.609999999999662 y[1] (closed_form) -4.842838615723596 y[1] (numeric) -4.8428386155555945 absolute error 1.680016126215378e-10 relative error 3.469073119142867e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.609999999999662 Order of pole (given) 0.5 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] 10.619999999999656 y[1] (closed_form) -4.841677108409015 y[1] (numeric) -4.841677108238394 absolute error 1.7062085078123346e-10 relative error 3.524003087378535e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.619999999999656 Order of pole (given) 0.5 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] 10.62999999999965 y[1] (closed_form) -4.840511639128885 y[1] (numeric) -4.8405116389556495 absolute error 1.7323564804883063e-10 relative error 3.578870602199537e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.62999999999965 Order of pole (given) 0.5 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] 10.639999999999645 y[1] (closed_form) -4.8393422110201545 y[1] (numeric) -4.8393422108443085 absolute error 1.758460044243293e-10 relative error 3.633675750888057e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.639999999999645 Order of pole (given) 0.5 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] 10.64999999999964 y[1] (closed_form) -4.838168827214809 y[1] (numeric) -4.838168827036355 absolute error 1.7845369626456886e-10 relative error 3.6884553358444785e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.64999999999964 Order of pole (given) 0.5 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] 10.659999999999634 y[1] (closed_form) -4.836991490839882 y[1] (numeric) -4.836991490658826 absolute error 1.8105605903429023e-10 relative error 3.7431543838182805e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.659999999999634 Order of pole (given) 0.5 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] 10.669999999999629 y[1] (closed_form) -4.8358102050174665 y[1] (numeric) -4.8358102048338125 absolute error 1.836539809119131e-10 relative error 3.797791334353035e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.669999999999629 Order of pole (given) 0.5 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] 10.679999999999623 y[1] (closed_form) -4.834624972864728 y[1] (numeric) -4.83462497267848 absolute error 1.8624835007585716e-10 relative error 3.852384644542487e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.679999999999623 Order of pole (given) 0.5 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] 10.689999999999618 y[1] (closed_form) -4.833435797493916 y[1] (numeric) -4.833435797305078 absolute error 1.8883827834770273e-10 relative error 3.9069160377719995e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.689999999999618 Order of pole (given) 0.5 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] 10.699999999999612 y[1] (closed_form) -4.832242682012373 y[1] (numeric) -4.832242681820949 absolute error 1.914237657274498e-10 relative error 3.961385599278965e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.699999999999612 Order of pole (given) 0.5 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] 10.709999999999607 y[1] (closed_form) -4.8310456295225475 y[1] (numeric) -4.831045629328543 absolute error 1.9400481221509835e-10 relative error 4.01579341394612e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.709999999999607 Order of pole (given) 0.5 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] 10.719999999999601 y[1] (closed_form) -4.829844643122011 y[1] (numeric) -4.829844642925428 absolute error 1.9658319416748782e-10 relative error 4.070176345059754e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.719999999999601 Order of pole (given) 0.5 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] 10.729999999999595 y[1] (closed_form) -4.828639725903459 y[1] (numeric) -4.828639725704303 absolute error 1.9915624704935908e-10 relative error 4.124479322426485e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.729999999999595 Order of pole (given) 0.5 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] 10.73999999999959 y[1] (closed_form) -4.827430880954731 y[1] (numeric) -4.8274308807530035 absolute error 2.0172752357439094e-10 relative error 4.1787760104499905e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.73999999999959 Order of pole (given) 0.5 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] 10.749999999999584 y[1] (closed_form) -4.826218111358818 y[1] (numeric) -4.8262181111545255 absolute error 2.042925828504849e-10 relative error 4.2329745182810744e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.749999999999584 Order of pole (given) 0.5 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] 10.759999999999579 y[1] (closed_form) -4.825001420193876 y[1] (numeric) -4.8250014199870215 absolute error 2.0685408941290007e-10 relative error 4.287130124918976e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.759999999999579 Order of pole (given) 0.5 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] 10.769999999999573 y[1] (closed_form) -4.8237808105332345 y[1] (numeric) -4.823780810323823 absolute error 2.0941115508321673e-10 relative error 4.3412245147197686e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.769999999999573 Order of pole (given) 0.5 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] 10.779999999999568 y[1] (closed_form) -4.822556285445411 y[1] (numeric) -4.822556285233446 absolute error 2.1196466803985459e-10 relative error 4.395276187435468e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.779999999999568 Order of pole (given) 0.5 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] 10.789999999999562 y[1] (closed_form) -4.821327847994121 y[1] (numeric) -4.821327847779607 absolute error 2.1451462828281365e-10 relative error 4.449285239377797e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.789999999999562 Order of pole (given) 0.5 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] 10.799999999999557 y[1] (closed_form) -4.82009550123829 y[1] (numeric) -4.820095501021228 absolute error 2.170619239905136e-10 relative error 4.50327019318912e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.799999999999557 Order of pole (given) 0.5 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] 10.809999999999551 y[1] (closed_form) -4.8188592482320605 y[1] (numeric) -4.8188592480124575 absolute error 2.1960300244927566e-10 relative error 4.557157433677762e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.809999999999551 Order of pole (given) 0.5 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] 10.819999999999546 y[1] (closed_form) -4.8176190920248105 y[1] (numeric) -4.817619091802669 absolute error 2.2214141637277862e-10 relative error 4.611020757961464e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.819999999999546 Order of pole (given) 0.5 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] 10.82999999999954 y[1] (closed_form) -4.816375035661159 y[1] (numeric) -4.816375035436484 absolute error 2.2467538940418308e-10 relative error 4.664823393956097e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.82999999999954 Order of pole (given) 0.5 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] 10.839999999999534 y[1] (closed_form) -4.815127082180979 y[1] (numeric) -4.815127081953773 absolute error 2.2720580972190874e-10 relative error 4.718583867967144e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.839999999999534 Order of pole (given) 0.5 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] 10.849999999999529 y[1] (closed_form) -4.813875234619408 y[1] (numeric) -4.813875234389675 absolute error 2.297326773259556e-10 relative error 4.772302274762188e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.849999999999529 Order of pole (given) 0.5 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] 10.859999999999523 y[1] (closed_form) -4.81261949600686 y[1] (numeric) -4.812619495774604 absolute error 2.3225599221632365e-10 relative error 4.8259787088722e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.859999999999523 Order of pole (given) 0.5 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] 10.869999999999518 y[1] (closed_form) -4.811359869369038 y[1] (numeric) -4.811359869134263 absolute error 2.347748662145932e-10 relative error 4.879594804563676e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.869999999999518 Order of pole (given) 0.5 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] 10.879999999999512 y[1] (closed_form) -4.810096357726939 y[1] (numeric) -4.810096357489649 absolute error 2.3729018749918396e-10 relative error 4.933169106228007e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.879999999999512 Order of pole (given) 0.5 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] 10.889999999999507 y[1] (closed_form) -4.8088289640968735 y[1] (numeric) -4.8088289638570725 absolute error 2.398010678916762e-10 relative error 4.986683237895367e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.889999999999507 Order of pole (given) 0.5 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] 10.899999999999501 y[1] (closed_form) -4.807557691490468 y[1] (numeric) -4.807557691248159 absolute error 2.4230839557048967e-10 relative error 5.0401557530840105e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.899999999999501 Order of pole (given) 0.5 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] 10.909999999999496 y[1] (closed_form) -4.806282542914682 y[1] (numeric) -4.806282542669872 absolute error 2.448095060003652e-10 relative error 5.09353130646175e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.909999999999496 Order of pole (given) 0.5 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] 10.91999999999949 y[1] (closed_form) -4.805003521371816 y[1] (numeric) -4.805003521124506 absolute error 2.4730972825182107e-10 relative error 5.146920853477643e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.91999999999949 Order of pole (given) 0.5 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] 10.929999999999485 y[1] (closed_form) -4.803720629859524 y[1] (numeric) -4.80372062960972 absolute error 2.49803733254339e-10 relative error 5.200213594886846e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.929999999999485 Order of pole (given) 0.5 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] 10.939999999999479 y[1] (closed_form) -4.8024338713708214 y[1] (numeric) -4.802433871118526 absolute error 2.5229507372159787e-10 relative error 5.253483556028268e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.939999999999479 Order of pole (given) 0.5 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] 10.949999999999473 y[1] (closed_form) -4.801143248894099 y[1] (numeric) -4.801143248639317 absolute error 2.547819732967582e-10 relative error 5.3066938453762035e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.949999999999473 Order of pole (given) 0.5 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] 10.959999999999468 y[1] (closed_form) -4.799848765413132 y[1] (numeric) -4.7998487651558674 absolute error 2.5726443197982007e-10 relative error 5.359844539970143e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.959999999999468 Order of pole (given) 0.5 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] 10.969999999999462 y[1] (closed_form) -4.79855042390709 y[1] (numeric) -4.798550423647346 absolute error 2.597442261276228e-10 relative error 5.412972735131396e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.969999999999462 Order of pole (given) 0.5 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] 10.979999999999457 y[1] (closed_form) -4.7972482273505515 y[1] (numeric) -4.797248227088332 absolute error 2.6221957938332707e-10 relative error 5.4660415087202405e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.979999999999457 Order of pole (given) 0.5 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] 10.989999999999451 y[1] (closed_form) -4.795942178713508 y[1] (numeric) -4.795942178448817 absolute error 2.646913799253525e-10 relative error 5.519069456261771e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.989999999999451 Order of pole (given) 0.5 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] 10.999999999999446 y[1] (closed_form) -4.794632280961381 y[1] (numeric) -4.794632280694221 absolute error 2.6716051593211887e-10 relative error 5.572075193189789e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 12.999999999999446 Order of pole (given) 0.5 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 Finished! diff ( y , x , 1 ) = ln ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 1001 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.19999999994447%