##############ECHO OF PROBLEM################# ##############temp/arccos_sqrtpostode.ode################# diff ( y , x , 1 ) = arccos ( 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(0.001) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=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=false $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(10.0) * (c(0.1) * c(x) + c(0.2)) * arccos(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) 2.532535480592211 y[1] (numeric) 2.532535480592211 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.010000000000000002 y[1] (closed_form) 2.543600721667676 y[1] (numeric) 2.5436007216806904 absolute error 1.3014478383865935e-11 relative error 5.1165571203853e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 0.02000000000000001 y[1] (closed_form) 2.5546534860587964 y[1] (numeric) 2.5546534860848196 absolute error 2.602318360800382e-11 relative error 1.0186580587158694e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.03000000000000002 y[1] (closed_form) 2.5656937968912934 y[1] (numeric) 2.5656937969303164 absolute error 3.90230070479447e-11 relative error 1.5209534004107068e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.04000000000000003 y[1] (closed_form) 2.5767216770859345 y[1] (numeric) 2.5767216771379498 absolute error 5.2015280971318134e-11 relative error 2.018661209469206e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.05000000000000004 y[1] (closed_form) 2.587737149360984 y[1] (numeric) 2.587737149425986 absolute error 6.500178173496352e-11 relative error 2.5119159320727397e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.060000000000000046 y[1] (closed_form) 2.598740236234604 y[1] (numeric) 2.598740236312585 absolute error 7.798073298204145e-11 relative error 3.000712879830966e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.07000000000000005 y[1] (closed_form) 2.6097309600272145 y[1] (numeric) 2.6097309601181666 absolute error 9.095213471255192e-11 relative error 3.485115366512856e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.08000000000000006 y[1] (closed_form) 2.6207093428638126 y[1] (numeric) 2.6207093429677286 absolute error 1.0391598692649495e-10 relative error 3.9651855025227435e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.09000000000000007 y[1] (closed_form) 2.631675406676253 y[1] (numeric) 2.6316754067931267 absolute error 1.1687362189150008e-10 relative error 4.441034847800962e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.10000000000000007 y[1] (closed_form) 2.6426291732054885 y[1] (numeric) 2.642629173335314 absolute error 1.2982548369677716e-10 relative error 4.912739366276648e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.11000000000000008 y[1] (closed_form) 2.6535706640037775 y[1] (numeric) 2.6535706641465486 absolute error 1.4277112825311633e-10 relative error 5.3803401654169436e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.12000000000000009 y[1] (closed_form) 2.6644999004368435 y[1] (numeric) 2.6644999005925545 absolute error 1.5571099964972746e-10 relative error 5.84391088264626e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.1300000000000001 y[1] (closed_form) 2.675416903686012 y[1] (numeric) 2.6754169038546545 absolute error 1.6864243335135143e-10 relative error 6.303407634115156e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.1400000000000001 y[1] (closed_form) 2.686321694750294 y[1] (numeric) 2.6863216949318653 absolute error 1.815712025177163e-10 relative error 6.759101222781666e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.1500000000000001 y[1] (closed_form) 2.6972142944484596 y[1] (numeric) 2.6972142946429534 absolute error 1.9449375443514327e-10 relative error 7.210912193200962e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.16000000000000011 y[1] (closed_form) 2.708094723421051 y[1] (numeric) 2.708094723628461 absolute error 2.0741008910363234e-10 relative error 7.658893439355684e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.17000000000000012 y[1] (closed_form) 2.7189630021323805 y[1] (numeric) 2.718963002352702 absolute error 2.2032153879081307e-10 relative error 8.10314589121011e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.18000000000000013 y[1] (closed_form) 2.7298191508724856 y[1] (numeric) 2.7298191511057137 absolute error 2.3322810349668543e-10 relative error 8.543719953834404e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.19000000000000014 y[1] (closed_form) 2.7406631897590596 y[1] (numeric) 2.740663190005189 absolute error 2.461293391320396e-10 relative error 8.980648919274083e-09% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.20000000000000015 y[1] (closed_form) 2.751495138739343 y[1] (numeric) 2.7514951389983695 absolute error 2.590265779645051e-10 relative error 9.41403000563482e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.21000000000000016 y[1] (closed_form) 2.7623150175919906 y[1] (numeric) 2.76231501786391 absolute error 2.7191937590487214e-10 relative error 9.843894493319376e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.22000000000000017 y[1] (closed_form) 2.773122845928907 y[1] (numeric) 2.7731228462137145 absolute error 2.8480773295314066e-10 relative error 1.0270289084785902e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.23000000000000018 y[1] (closed_form) 2.7839186431970475 y[1] (numeric) 2.7839186434947383 absolute error 2.9769076093089097e-10 relative error 1.0693227751405242e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.24000000000000019 y[1] (closed_form) 2.794702428680198 y[1] (numeric) 2.7947024289907674 absolute error 3.105693480165428e-10 relative error 1.1112787709681478e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.25000000000000017 y[1] (closed_form) 2.8054742215007202 y[1] (numeric) 2.805474221824166 absolute error 3.2344571465614536e-10 relative error 1.1529092378654113e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2600000000000002 y[1] (closed_form) 2.816234040621273 y[1] (numeric) 2.8162340409575912 absolute error 3.3631808449285927e-10 relative error 1.194212127407799e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2700000000000002 y[1] (closed_form) 2.8269819048465052 y[1] (numeric) 2.8269819051956926 absolute error 3.4918734570510424e-10 relative error 1.2351948383768088e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2800000000000002 y[1] (closed_form) 2.8377178328247203 y[1] (numeric) 2.8377178331867734 absolute error 3.620530542036704e-10 relative error 1.27585995343052e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2900000000000002 y[1] (closed_form) 2.848441843049515 y[1] (numeric) 2.848441843424431 absolute error 3.7491609816697746e-10 relative error 1.3162146844662128e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3000000000000002 y[1] (closed_form) 2.8591539538613966 y[1] (numeric) 2.859153954249172 absolute error 3.8777558941660573e-10 relative error 1.356259913506581e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3100000000000002 y[1] (closed_form) 2.8698541834493714 y[1] (numeric) 2.8698541838500033 absolute error 4.0063197204176504e-10 relative error 1.3960011430275263e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.32000000000000023 y[1] (closed_form) 2.880542549852506 y[1] (numeric) 2.880542550265991 absolute error 4.134852460424554e-10 relative error 1.4354422435579968e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.33000000000000024 y[1] (closed_form) 2.8912190709614696 y[1] (numeric) 2.891219071387806 absolute error 4.263362995970965e-10 relative error 1.4745900920448729e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.34000000000000025 y[1] (closed_form) 2.90188376452005 y[1] (numeric) 2.901883764959235 absolute error 4.391846886164785e-10 relative error 1.513446865054281e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.35000000000000026 y[1] (closed_form) 2.9125366481266495 y[1] (numeric) 2.9125366485786794 absolute error 4.520299690113916e-10 relative error 1.5520146992901817e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.36000000000000026 y[1] (closed_form) 2.9231777392357476 y[1] (numeric) 2.9231777397006224 absolute error 4.648748053170948e-10 relative error 1.5903063268353786e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3700000000000003 y[1] (closed_form) 2.9338070551593582 y[1] (numeric) 2.933807055637075 absolute error 4.777165329983291e-10 relative error 1.6283161231009465e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3800000000000003 y[1] (closed_form) 2.944424613068448 y[1] (numeric) 2.9444246135590055 absolute error 4.905573725011436e-10 relative error 1.666055127795998e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3900000000000003 y[1] (closed_form) 2.9550304299943475 y[1] (numeric) 2.9550304304977435 absolute error 5.033959915579089e-10 relative error 1.703522192016384e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4000000000000003 y[1] (closed_form) 2.965624522830128 y[1] (numeric) 2.9656245233463614 absolute error 5.162332783470447e-10 relative error 1.7407236633395436e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4100000000000003 y[1] (closed_form) 2.9762069083319687 y[1] (numeric) 2.9762069088610366 absolute error 5.290679006009213e-10 relative error 1.7776583312127327e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4200000000000003 y[1] (closed_form) 2.9867776031204936 y[1] (numeric) 2.986777603662397 absolute error 5.419034110332177e-10 relative error 1.8143413505814885e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4300000000000003 y[1] (closed_form) 2.997336623682104 y[1] (numeric) 2.9973366242368398 absolute error 5.547358128410451e-10 relative error 1.8507624684463206e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.44000000000000034 y[1] (closed_form) 3.0078839863702678 y[1] (numeric) 3.0078839869378355 absolute error 5.675677705596627e-10 relative error 1.886933715301198e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.45000000000000034 y[1] (closed_form) 3.018419707406812 y[1] (numeric) 3.0184197079872113 absolute error 5.803992841890704e-10 relative error 1.92285811931603e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.46000000000000035 y[1] (closed_form) 3.028943802883184 y[1] (numeric) 3.0289438034764142 absolute error 5.932303537292682e-10 relative error 1.9585386601249768e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.47000000000000036 y[1] (closed_form) 3.0394562887616985 y[1] (numeric) 3.0394562893677586 absolute error 6.060600910018366e-10 relative error 1.993975347639399e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.48000000000000037 y[1] (closed_form) 3.049957180876763 y[1] (numeric) 3.049957181495654 absolute error 6.188911605420344e-10 relative error 2.0291798338103993e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4900000000000004 y[1] (closed_form) 3.060446494936092 y[1] (numeric) 3.0604464955678123 absolute error 6.317204537253929e-10 relative error 2.0641447408757407e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.001 Finished! diff ( y , x , 1 ) = arccos ( 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%