##############ECHO OF PROBLEM################# ##############R:Temp/arcsin_sqrtpostode.ode################# diff ( y , x , 1 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.0) x_end=c(0.5) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=c(0.01) # 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) #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(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arcsin(sqrt ( c(0.1) * c(x) + c(0.2))) + c(5.0) * sqrt( c(0.1) * c(x) + c(0.2)) * sqrt( c(0.8) - c(0.1) * c(x)) - c(5.0) * arcsin(sqrt( c(0.1) * c(x) + c(0.2)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (closed_form) 0.609057172997582 y[1] (numeric) 0.609057172997582 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 14 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 2.0 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] 0.010000000000000002 y[1] (closed_form) 0.6136998951900665 y[1] (numeric) 0.613699895177051 absolute error 1.3015477584588098e-11 relative error 2.1208212167866066e-09% Desired digits 12 Estimated correct digits 13 Correct digits 11 h 0.001 Radius of convergence (given) for eq 1 2.01 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] 0.02000000000000001 y[1] (closed_form) 0.6183550940668949 y[1] (numeric) 0.6183550940408706 absolute error 2.6024293831028444e-11 relative error 4.208632560923495e-09% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 2.02 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] 0.03000000000000002 y[1] (closed_form) 0.6230227465023472 y[1] (numeric) 0.6230227464633225 absolute error 3.90247834047841e-11 relative error 6.263781478905775e-09% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 2.03 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] 0.04000000000000003 y[1] (closed_form) 0.6277028295756555 y[1] (numeric) 0.6277028295236377 absolute error 5.201783448427477e-11 relative error 8.287016089992819e-09% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 2.04 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] 0.05000000000000004 y[1] (closed_form) 0.6323953205685546 y[1] (numeric) 0.6323953205035511 absolute error 6.500355809180292e-11 relative error 1.0278943562289725e-08% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 2.05 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] 0.060000000000000046 y[1] (closed_form) 0.6371001969628827 y[1] (numeric) 0.6371001968849014 absolute error 7.798128809355376e-11 relative error 1.2240035156996966e-08% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 2.06 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] 0.07000000000000005 y[1] (closed_form) 0.6418174364382216 y[1] (numeric) 0.6418174363472684 absolute error 9.095324493557655e-11 relative error 1.4171201929371592e-08% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 2.07 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] 0.08000000000000006 y[1] (closed_form) 0.6465470168695724 y[1] (numeric) 0.6465470167656547 absolute error 1.0391765226103189e-10 relative error 1.60727139016396e-08% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 2.08 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] 0.09000000000000007 y[1] (closed_form) 0.6512889163250812 y[1] (numeric) 0.6512889162082056 absolute error 1.168756202929444e-10 relative error 1.7945280099716556e-08% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 2.09 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] 0.10000000000000007 y[1] (closed_form) 0.6560431130637943 y[1] (numeric) 0.6560431129339668 absolute error 1.2982748209822148e-10 relative error 1.9789474123417394e-08% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 2.1 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] 0.11000000000000008 y[1] (closed_form) 0.660809585533455 y[1] (numeric) 0.6608095853906816 absolute error 1.4277345972146804e-10 relative error 2.1605839692263332e-08% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 2.11 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] 0.12000000000000009 y[1] (closed_form) 0.665588312368337 y[1] (numeric) 0.6655883122126249 absolute error 1.5571210987275208e-10 relative error 2.3394658076054207e-08% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 2.12 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] 0.1300000000000001 y[1] (closed_form) 0.6703792723871183 y[1] (numeric) 0.6703792722184735 absolute error 1.6864476481970314e-10 relative error 2.5156619807051145e-08% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 2.13 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] 0.1400000000000001 y[1] (closed_form) 0.675182444590785 y[1] (numeric) 0.6751824444092118 absolute error 1.8157320091916063e-10 relative error 2.6892464751391548e-08% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 2.14 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] 0.1500000000000001 y[1] (closed_form) 0.6799978081605684 y[1] (numeric) 0.6799978079660729 absolute error 1.9449553079198267e-10 relative error 2.8602376133844286e-08% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 2.15 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] 0.16000000000000011 y[1] (closed_form) 0.6848253424559259 y[1] (numeric) 0.6848253422485134 absolute error 2.0741242057198406e-10 relative error 3.028690787466481e-08% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 2.16 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] 0.17000000000000012 y[1] (closed_form) 0.6896650270125453 y[1] (numeric) 0.6896650267922213 absolute error 2.2032398128146724e-10 relative error 3.194652079660398e-08% Desired digits 12 Estimated correct digits 13 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.17 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] 0.18000000000000013 y[1] (closed_form) 0.6945168415403891 y[1] (numeric) 0.6945168413071584 absolute error 2.3323065700964207e-10 relative error 3.358171365468302e-08% Desired digits 12 Estimated correct digits 13 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.18 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] 0.19000000000000014 y[1] (closed_form) 0.6993807659217648 y[1] (numeric) 0.6993807656756319 absolute error 2.461328918457184e-10 relative error 3.519297410493152e-08% Desired digits 12 Estimated correct digits 13 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.19 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] 0.20000000000000015 y[1] (closed_form) 0.7042567802094295 y[1] (numeric) 0.7042567799504005 absolute error 2.590290204551593e-10 relative error 3.6780479469168915e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.2 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] 0.21000000000000016 y[1] (closed_form) 0.7091448646247316 y[1] (numeric) 0.709144864352809 absolute error 2.7192259555164355e-10 relative error 3.834514062166138e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.21 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] 0.22000000000000017 y[1] (closed_form) 0.7140449995557643 y[1] (numeric) 0.7140449992709537 absolute error 2.848106195330047e-10 relative error 3.988692865438406e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.22 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] 0.23000000000000018 y[1] (closed_form) 0.7189571655555724 y[1] (numeric) 0.7189571652578782 absolute error 2.976942026222673e-10 relative error 4.140638926551693e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.23 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] 0.24000000000000019 y[1] (closed_form) 0.7238813433403708 y[1] (numeric) 0.7238813430297969 absolute error 3.1057389993094375e-10 relative error 4.2903979055157265e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.24 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] 0.25000000000000017 y[1] (closed_form) 0.7288175137877979 y[1] (numeric) 0.7288175134643475 absolute error 3.234503775928488e-10 relative error 4.438015984437833e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.25 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] 0.2600000000000002 y[1] (closed_form) 0.7337656579351934 y[1] (numeric) 0.7337656575988706 absolute error 3.3632285845186516e-10 relative error 4.583518659053533e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.2600000000000002 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] 0.2700000000000002 y[1] (closed_form) 0.7387257569779107 y[1] (numeric) 0.7387257566287182 absolute error 3.491924527310175e-10 relative error 4.726956511703965e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.27 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] 0.2800000000000002 y[1] (closed_form) 0.7436977922676444 y[1] (numeric) 0.743697791905587 absolute error 3.6205738407346644e-10 relative error 4.868340175778927e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.2800000000000002 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] 0.2900000000000002 y[1] (closed_form) 0.7486817453107992 y[1] (numeric) 0.7486817449358788 absolute error 3.749204280367735e-10 relative error 5.0077410112508254e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.29 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] 0.3000000000000002 y[1] (closed_form) 0.7536775977668664 y[1] (numeric) 0.7536775973790861 absolute error 3.8778025235330915e-10 relative error 5.145174189896254e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.3000000000000003 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] 0.3100000000000002 y[1] (closed_form) 0.7586853314468405 y[1] (numeric) 0.7586853310462041 absolute error 4.0063641293386354e-10 relative error 5.280666388657276e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.31 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] 0.32000000000000023 y[1] (closed_form) 0.7637049283116548 y[1] (numeric) 0.7637049278981651 absolute error 4.134896869345539e-10 relative error 5.414259769786583e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.3200000000000003 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] 0.33000000000000024 y[1] (closed_form) 0.7687363704706405 y[1] (numeric) 0.7687363700442998 absolute error 4.2634062946689255e-10 relative error 5.545992694555036e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.33 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] 0.34000000000000025 y[1] (closed_form) 0.7737796401800079 y[1] (numeric) 0.7737796397408191 absolute error 4.3918879644166964e-10 relative error 5.675889796473569e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.3400000000000003 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] 0.35000000000000026 y[1] (closed_form) 0.7788347198413588 y[1] (numeric) 0.7788347193893231 absolute error 4.5203563114881717e-10 relative error 5.803999483239429e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.35 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] 0.36000000000000026 y[1] (closed_form) 0.783901592000209 y[1] (numeric) 0.7839015915353297 absolute error 4.6487935723149576e-10 relative error 5.930328015348281e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.3600000000000003 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] 0.3700000000000003 y[1] (closed_form) 0.7889802393445478 y[1] (numeric) 0.7889802388668261 absolute error 4.777216400242423e-10 relative error 6.054925284581446e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.37 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] 0.3800000000000003 y[1] (closed_form) 0.7940706447034058 y[1] (numeric) 0.7940706442128441 absolute error 4.905617023709397e-10 relative error 6.177809312597998e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.3800000000000003 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] 0.3900000000000003 y[1] (closed_form) 0.7991727910454558 y[1] (numeric) 0.799172790542055 absolute error 5.034007655169148e-10 relative error 6.299022829072794e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.39 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] 0.4000000000000003 y[1] (closed_form) 0.8042866614776245 y[1] (numeric) 0.8042866609613865 absolute error 5.162380523060506e-10 relative error 6.418582789345594e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.4000000000000004 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] 0.4100000000000003 y[1] (closed_form) 0.8094122392437333 y[1] (numeric) 0.8094122387146597 absolute error 5.290735627383469e-10 relative error 6.536515474891779e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.41 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] 0.4200000000000003 y[1] (closed_form) 0.8145495077231564 y[1] (numeric) 0.8145495071812481 absolute error 5.419082960145261e-10 relative error 6.65285892234197e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.4200000000000004 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] 0.4300000000000003 y[1] (closed_form) 0.8196984504294957 y[1] (numeric) 0.819698449874754 absolute error 5.547416970230756e-10 relative error 6.76763139825882e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.43 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] 0.44000000000000034 y[1] (closed_form) 0.8248590510092804 y[1] (numeric) 0.8248590504417072 absolute error 5.675732106524833e-10 relative error 6.880850855161407e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.4400000000000004 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] 0.45000000000000034 y[1] (closed_form) 0.8300312932406859 y[1] (numeric) 0.8300312926602806 absolute error 5.804052793934034e-10 relative error 6.992571052680806e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.45 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] 0.46000000000000035 y[1] (closed_form) 0.8352151610322625 y[1] (numeric) 0.8352151604390268 absolute error 5.932356827997864e-10 relative error 7.102788724124599e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.4600000000000004 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] 0.47000000000000036 y[1] (closed_form) 0.8404106384216976 y[1] (numeric) 0.840410637815631 absolute error 6.060666413176818e-10 relative error 7.211553657339263e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.47 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] 0.48000000000000037 y[1] (closed_form) 0.8456177095745812 y[1] (numeric) 0.845617708955685 absolute error 6.188961565456452e-10 relative error 7.318864654064584e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.4800000000000004 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] 0.4900000000000004 y[1] (closed_form) 0.850836358783202 y[1] (numeric) 0.8508363581514757 absolute error 6.317262268851209e-10 relative error 7.424767646137798e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.49 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 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 500 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.20000000000007%