##############ECHO OF PROBLEM################# ##############R:Temp/tan_sqrtpostode.ode################# diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(1.4) x_end=c(2.1) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=c(0.0001) # 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 # 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 # ELIMINATED in preodein.rb #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=12 $glob_max_minutes=(3.0) $glob_subiter_method=2 $glob_max_iter=1000000 $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) $glob_h_reason=1 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(tan(sqrt(c(2.0)*c(x) + c(1.0)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 1.4 y[1] (closed_form) -2.514161640922489 y[1] (numeric) -2.514161640922489 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 3.4 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] 1.4099999999999988 y[1] (closed_form) -2.477131584442638 y[1] (numeric) -2.4770842028283395 absolute error 4.738161429829191e-05 relative error 0.0019127613000402203% Desired digits 12 Estimated correct digits 13 Correct digits 5 h 0.001 Radius of convergence (given) for eq 1 3.409999999999999 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] 1.4199999999999977 y[1] (closed_form) -2.4411228419178475 y[1] (numeric) -2.441030178933042 absolute error 9.266298480525847e-05 relative error 0.0037959165026065864% Desired digits 12 Estimated correct digits 13 Correct digits 4 h 0.001 Radius of convergence (given) for eq 1 3.4199999999999977 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] 1.4299999999999966 y[1] (closed_form) -2.4060915775405896 y[1] (numeric) -2.405955612058374 absolute error 0.00013596548221572746 relative error 0.0056508855890974% Desired digits 12 Estimated correct digits 12 Correct digits 4 h 0.001 Radius of convergence (given) for eq 1 3.4299999999999966 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] 1.4399999999999955 y[1] (closed_form) -2.37199643510759 y[1] (numeric) -2.3718190332427453 absolute error 0.00017740186484482834 relative error 0.007479010601328397% Desired digits 12 Estimated correct digits 12 Correct digits 4 h 0.001 Radius of convergence (given) for eq 1 3.4399999999999955 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] 1.4499999999999944 y[1] (closed_form) -2.3387983649807493 y[1] (numeric) -2.3385812879807464 absolute error 0.00021707700000295205 relative error 0.009281561132130295% Desired digits 12 Estimated correct digits 12 Correct digits 4 h 0.001 Radius of convergence (given) for eq 1 3.4499999999999944 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] 1.4599999999999933 y[1] (closed_form) -2.306460465341871 y[1] (numeric) -2.3062053768259028 absolute error 0.00025508851596844906 relative error 0.011059739362609842% Desired digits 12 Estimated correct digits 12 Correct digits 4 h 0.001 Radius of convergence (given) for eq 1 3.4599999999999933 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] 1.4699999999999922 y[1] (closed_form) -2.274947836382328 y[1] (numeric) -2.2746563089902603 absolute error 0.00029152739206761424 relative error 0.012814684688823788% Desired digits 12 Estimated correct digits 12 Correct digits 4 h 0.001 Radius of convergence (given) for eq 1 3.469999999999992 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] 1.479999999999991 y[1] (closed_form) -2.2442274462144147 y[1] (numeric) -2.2439009677209456 absolute error 0.00032647849346911784 relative error 0.014547477975987906% Desired digits 12 Estimated correct digits 12 Correct digits 4 h 0.001 Radius of convergence (given) for eq 1 3.479999999999991 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] 1.48999999999999 y[1] (closed_form) -2.214268007419532 y[1] (numeric) -2.213907986362986 absolute error 0.00036002105654597827 relative error 0.016259145475598518% Desired digits 12 Estimated correct digits 12 Correct digits 4 h 0.001 Radius of convergence (given) for eq 1 3.48999999999999 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] 1.499999999999989 y[1] (closed_form) -2.185039863261551 y[1] (numeric) -2.184647634131614 absolute error 0.0003922291299369718 relative error 0.017950662435581466% Desired digits 12 Estimated correct digits 12 Correct digits 4 h 0.001 Radius of convergence (given) for eq 1 3.499999999999989 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] 1.5099999999999878 y[1] (closed_form) -2.156514882693875 y[1] (numeric) -2.1560917107179907 absolute error 0.00042317197588426225 relative error 0.019622956432169127% Desired digits 12 Estimated correct digits 12 Correct digits 4 h 0.001 Radius of convergence (given) for eq 1 3.509999999999988 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] 1.5199999999999867 y[1] (closed_form) -2.1286663633773486 y[1] (numeric) -2.1282134489414957 absolute error 0.0004529144358529358 relative error 0.02127691044708107% Desired digits 12 Estimated correct digits 12 Correct digits 4 h 0.001 Radius of convergence (given) for eq 1 3.5199999999999867 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] 1.5299999999999856 y[1] (closed_form) -2.1014689420048454 y[1] (numeric) -2.100987424740807 absolute error 0.00048151726403844464 relative error 0.02291336571355973% Desired digits 12 Estimated correct digits 12 Correct digits 4 h 0.001 Radius of convergence (given) for eq 1 3.5299999999999856 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] 1.5399999999999845 y[1] (closed_form) -2.074898511298209 y[1] (numeric) -2.0743894738662707 absolute error 0.0005090374319380864 relative error 0.02453312435120478% Desired digits 12 Estimated correct digits 12 Correct digits 4 h 0.001 Radius of convergence (given) for eq 1 3.5399999999999845 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] 1.5499999999999834 y[1] (closed_form) -2.048932143105383 y[1] (numeric) -2.0483966146985852 absolute error 0.0005355284067976029 relative error 0.026136951806805593% Desired digits 12 Estimated correct digits 12 Correct digits 4 h 0.001 Radius of convergence (given) for eq 1 3.5499999999999834 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] 1.5599999999999823 y[1] (closed_form) -2.0235480170809854 y[1] (numeric) -2.022986976674505 absolute error 0.0005610404064801955 relative error 0.027725579118676374% Desired digits 12 Estimated correct digits 12 Correct digits 4 h 0.001 Radius of convergence (given) for eq 1 3.5599999999999823 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] 1.5699999999999812 y[1] (closed_form) -1.9987253544830008 y[1] (numeric) -1.9981397338499827 absolute error 0.0005856206330181468 relative error 0.02929970501973374% Desired digits 12 Estimated correct digits 12 Correct digits 4 h 0.001 Radius of convergence (given) for eq 1 3.569999999999981 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] 1.57999999999998 y[1] (closed_form) -1.9744443566624243 y[1] (numeric) -1.9738350431756002 absolute error 0.0006093134868241368 relative error 0.030859997890956652% Desired digits 12 Estimated correct digits 12 Correct digits 4 h 0.001 Radius of convergence (given) for eq 1 3.57999999999998 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] 1.589999999999979 y[1] (closed_form) -1.9506861478622486 y[1] (numeric) -1.950053987098845 absolute error 0.0006321607634036663 relative error 0.03240709757930303% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.589999999999979 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] 1.5999999999999779 y[1] (closed_form) -1.9274327219775935 y[1] (numeric) -1.9267785201434366 absolute error 0.0006542018341568756 relative error 0.03394161708978606% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.599999999999978 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] 1.6099999999999768 y[1] (closed_form) -1.9046668929605788 y[1] (numeric) -1.90399141914784 absolute error 0.0006754738127388027 relative error 0.03546414416270232% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.609999999999977 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] 1.6199999999999757 y[1] (closed_form) -1.8823722485820893 y[1] (numeric) -1.8816762368738178 absolute error 0.0006960117082714934 relative error 0.03697524274466803% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.6199999999999757 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] 1.6299999999999746 y[1] (closed_form) -1.8605331072882825 y[1] (numeric) -1.8598172587216935 absolute error 0.0007158485665890169 relative error 0.0384754543622372% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.6299999999999746 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] 1.6399999999999735 y[1] (closed_form) -1.839134477912795 y[1] (numeric) -1.8383994623122497 absolute error 0.0007350156005452302 relative error 0.039965299404282166% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.6399999999999735 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] 1.6499999999999724 y[1] (closed_form) -1.818162022026551 y[1] (numeric) -1.817408479716169 absolute error 0.0007535423103821604 relative error 0.041445278322459436% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.6499999999999724 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] 1.6599999999999713 y[1] (closed_form) -1.797602018725817 y[1] (numeric) -1.7968305621308376 absolute error 0.0007714565949794583 relative error 0.04291587275398617% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.6599999999999713 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] 1.6699999999999702 y[1] (closed_form) -1.7774413316762498 y[1] (numeric) -1.776652546821471 absolute error 0.0007887848547789567 relative error 0.04437754657337005% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.66999999999997 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] 1.679999999999969 y[1] (closed_form) -1.7576673782460641 y[1] (numeric) -1.7568618261589697 absolute error 0.0008055520870944299 relative error 0.04583074687875654% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.679999999999969 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] 1.689999999999968 y[1] (closed_form) -1.7382681005753933 y[1] (numeric) -1.737446318600975 absolute error 0.0008217819744182897 relative error 0.047275904916293826% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.689999999999968 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] 1.6999999999999669 y[1] (closed_form) -1.7192319384416317 y[1] (numeric) -1.7183944414752839 absolute error 0.0008374969663478282 relative error 0.04871343694946495% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.699999999999967 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] 1.7099999999999658 y[1] (closed_form) -1.7005478037919448 y[1] (numeric) -1.6996950854363435 absolute error 0.0008527183556013007 relative error 0.05014374507437412% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.7099999999999658 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] 1.7199999999999647 y[1] (closed_form) -1.6822050568246882 y[1] (numeric) -1.6813375904760324 absolute error 0.0008674663486558654 relative error 0.05156721798787631% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.7199999999999647 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] 1.7299999999999636 y[1] (closed_form) -1.6641934835108663 y[1] (numeric) -1.6633117233794787 absolute error 0.0008817601313875212 relative error 0.052984231708882536% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.7299999999999636 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] 1.7399999999999625 y[1] (closed_form) -1.6465032744555248 y[1] (numeric) -1.6456076565253566 absolute error 0.0008956179301682354 relative error 0.054395150259534314% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.7399999999999625 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] 1.7499999999999614 y[1] (closed_form) -1.629125005006734 y[1] (numeric) -1.6282159479380176 absolute error 0.0009090570687164679 relative error 0.05580032630539056% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.7499999999999614 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] 1.7599999999999603 y[1] (closed_form) -1.6120496165271219 y[1] (numeric) -1.611127522506044 absolute error 0.0009220940210779016 relative error 0.05720010176016738% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.7599999999999603 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] 1.7699999999999592 y[1] (closed_form) -1.5952683987494263 y[1] (numeric) -1.5943336542884012 absolute error 0.0009347444610250388 relative error 0.058594808356876506% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.769999999999959 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] 1.779999999999958 y[1] (closed_form) -1.5787729731435338 y[1] (numeric) -1.5778259498354046 absolute error 0.0009470233081292356 relative error 0.0599847681863716% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.779999999999958 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] 1.789999999999957 y[1] (closed_form) -1.562555277228009 y[1] (numeric) -1.561596332457219 absolute error 0.000958944770789838 relative error 0.06137029420751227% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.789999999999957 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] 1.7999999999999559 y[1] (closed_form) -1.5466075497640877 y[1] (numeric) -1.5456370273776723 absolute error 0.0009705223864153734 relative error 0.0627516907287445% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.799999999999956 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] 1.8099999999999548 y[1] (closed_form) -1.5309223167747728 y[1] (numeric) -1.5299405477157784 absolute error 0.0009817690589943862 relative error 0.06412925386460498% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.8099999999999548 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] 1.8199999999999537 y[1] (closed_form) -1.5154923783358651 y[1] (numeric) -1.5144996812416214 absolute error 0.0009926970942437663 relative error 0.06550327196853534% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.8199999999999537 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] 1.8299999999999526 y[1] (closed_form) -1.5003107960896322 y[1] (numeric) -1.499307477857136 absolute error 0.0010033182324962198 relative error 0.06687402604255333% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.8299999999999526 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] 1.8399999999999515 y[1] (closed_form) -1.4853708814354107 y[1] (numeric) -1.4843572377559058 absolute error 0.0010136436795049608 relative error 0.06824179012620812% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.8399999999999515 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] 1.8499999999999504 y[1] (closed_form) -1.4706661843546995 y[1] (numeric) -1.469642500219383 absolute error 0.001023684135316616 relative error 0.06960683166627574% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.8499999999999504 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] 1.8599999999999492 y[1] (closed_form) -1.4561904828313064 y[1] (numeric) -1.455157033009969 absolute error 0.001033449821337351 relative error 0.07096941186760056% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.8599999999999492 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] 1.8699999999999481 y[1] (closed_form) -1.4419377728299092 y[1] (numeric) -1.440894822324175 absolute error 0.0010429505057341082 relative error 0.07232978602725976% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.869999999999948 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] 1.879999999999947 y[1] (closed_form) -1.4279022587989179 y[1] (numeric) -1.4268500632716483 absolute error 0.0010521955272695394 relative error 0.07368820385189356% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.879999999999947 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] 1.889999999999946 y[1] (closed_form) -1.414078344665924 y[1] (numeric) -1.4130171508482225 absolute error 0.0010611938177014224 relative error 0.07504490976079048% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.889999999999946 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] 1.8999999999999448 y[1] (closed_form) -1.4004606252961644 y[1] (numeric) -1.3993906713733368 absolute error 0.0010699539228276045 relative error 0.07640014317441694% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.899999999999945 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] 1.9099999999999437 y[1] (closed_form) -1.3870438783864496 y[1] (numeric) -1.3859653943641768 absolute error 0.001078484022272841 relative error 0.07775413878957045% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.9099999999999437 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] 1.9199999999999426 y[1] (closed_form) -1.3738230567688703 y[1] (numeric) -1.3727362648207666 absolute error 0.0010867919481036825 relative error 0.07910712684206483% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.9199999999999426 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] 1.9299999999999415 y[1] (closed_form) -1.3607932811003196 y[1] (numeric) -1.3596983958979572 absolute error 0.00109488520236245 relative error 0.08045933335863771% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.9299999999999415 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] 1.9399999999999404 y[1] (closed_form) -1.3479498329154171 y[1] (numeric) -1.3468470619418547 absolute error 0.0011027709735624835 relative error 0.08181098039660364% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.9399999999999404 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] 1.9499999999999393 y[1] (closed_form) -1.3352881480219563 y[1] (numeric) -1.3341776918697146 absolute error 0.0011104561522417011 relative error 0.08316228627406658% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.9499999999999393 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] 1.9599999999999382 y[1] (closed_form) -1.3228038102193087 y[1] (numeric) -1.3216858628736863 absolute error 0.0011179473456224276 relative error 0.084513465790296% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.9599999999999382 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] 1.9699999999999371 y[1] (closed_form) -1.310492545321511 y[1] (numeric) -1.309367294430068 absolute error 0.001125250891442997 relative error 0.08586473043743507% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.969999999999937 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] 1.979999999999936 y[1] (closed_form) -1.2983502154679145 y[1] (numeric) -1.297217842596918 absolute error 0.0011323728709964342 relative error 0.08721628860271237% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.979999999999936 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] 1.989999999999935 y[1] (closed_form) -1.2863728137053934 y[1] (numeric) -1.2852334945839392 absolute error 0.001139319121454152 relative error 0.08856834576380283% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.989999999999935 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] 1.9999999999999338 y[1] (closed_form) -1.2745564588270966 y[1] (numeric) -1.2734103635795955 absolute error 0.0011460952475010888 relative error 0.08992110467634966% Desired digits 12 Estimated correct digits 12 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 3.999999999999934 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] 2.0099999999999327 y[1] (closed_form) -1.2628973904536653 y[1] (numeric) -1.261744683821342 absolute error 0.0011527066323233637 relative error 0.09127476555393639% Desired digits 12 Estimated correct digits 11 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 4.009999999999932 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] 2.0199999999999316 y[1] (closed_form) -1.2513919643437499 y[1] (numeric) -1.2502328058957402 absolute error 0.0011591584480097339 relative error 0.09262952624261218% Desired digits 12 Estimated correct digits 11 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 4.019999999999932 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] 2.0299999999999305 y[1] (closed_form) -1.2400366479214138 y[1] (numeric) -1.2388711922560427 absolute error 0.0011654556653710735 relative error 0.09398558238779836% Desired digits 12 Estimated correct digits 11 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 4.02999999999993 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] 2.0399999999999294 y[1] (closed_form) -1.2288280160088425 y[1] (numeric) -1.2276564129455925 absolute error 0.0011716030632500374 relative error 0.09534312759692212% Desired digits 12 Estimated correct digits 11 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 4.03999999999993 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] 2.0499999999999283 y[1] (closed_form) -1.2177627467534065 y[1] (numeric) -1.216585141516086 absolute error 0.001177605237320467 relative error 0.0967023535955587% Desired digits 12 Estimated correct digits 11 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 4.049999999999928 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] 2.0599999999999272 y[1] (closed_form) -1.2068376177388487 y[1] (numeric) -1.2056541511304248 absolute error 0.0011834666084238332 relative error 0.09806345037878386% Desired digits 12 Estimated correct digits 11 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 4.059999999999928 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] 2.069999999999926 y[1] (closed_form) -1.196049502270946 y[1] (numeric) -1.1948603108404743 absolute error 0.0011891914304718032 relative error 0.09942660635817152% Desired digits 12 Estimated correct digits 11 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 4.069999999999926 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] 2.079999999999925 y[1] (closed_form) -1.1853953658285692 y[1] (numeric) -1.1842005820306398 absolute error 0.0011947837979293663 relative error 0.10079200850378175% Desired digits 12 Estimated correct digits 11 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 4.0799999999999255 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] 2.089999999999924 y[1] (closed_form) -1.1748722626716164 y[1] (numeric) -1.1736720150187039 absolute error 0.0012002476529124895 relative error 0.10215984248220912% Desired digits 12 Estimated correct digits 11 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 4.0899999999999235 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] 2.099999999999923 y[1] (closed_form) -1.1644773325977864 y[1] (numeric) -1.163271745805861 absolute error 0.0012055867919253949 relative error 0.10353029279117859% Desired digits 12 Estimated correct digits 11 Correct digits 3 h 0.001 Radius of convergence (given) for eq 1 4.099999999999923 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 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; Iterations 701 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.28571428570322%