##############ECHO OF PROBLEM################# ##############temp/mtest2postode.ode################# diff ( y1 , x , 1 ) = neg ( y2 ) ; diff ( y2 , x , 1 ) = y1 ; ! #BEGIN FIRST INPUT BLOCK # Digits:=64; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.2) x_end=c(0.8) $array_y1_init[0 + 1] = exact_soln_y1(x_start) $array_y2_init[0 + 1] = exact_soln_y2(x_start) $glob_max_h=0.00001 $glob_look_poles=true # 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=3 #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_y1 (x) x = c(x) return(cos(c(x))) end def exact_soln_y2 (x) x = c(x) return(sin(c(x))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.2 y1[1] (closed_form) 0.9800665778412416 y1[1] (numeric) 0.9800665778412416 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 y2[1] (closed_form) 0.19866933079506122 y2[1] (numeric) 0.19866933079506122 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.21000000000000002 y1[1] (closed_form) 0.9780309147241483 y1[1] (numeric) 0.9780798845332912 absolute error 4.8969809142929144e-05 relative error 0.00500697967780916% Desired digits 8 Estimated correct digits 13 Correct digits 5 h 0.001 y2[1] (closed_form) 0.20845989984609958 y2[1] (numeric) 0.19866933079506122 absolute error 0.009790569051038367 relative error 4.696619857472101% Desired digits 8 Estimated correct digits 13 Correct digits 3 h 0.001 TOP MAIN SOLVE Loop x[1] 0.22000000000000003 y1[1] (closed_form) 0.9758974493306055 y1[1] (numeric) 0.9760931912253408 absolute error 0.00019574189473525738 relative error 0.020057629504977397% Desired digits 8 Estimated correct digits 13 Correct digits 4 h 0.001 y2[1] (closed_form) 0.21822962308086935 y2[1] (numeric) 0.19866933079506122 absolute error 0.019560292285808134 relative error 8.963170081891072% Desired digits 8 Estimated correct digits 13 Correct digits 3 h 0.001 TOP MAIN SOLVE Loop x[1] 0.23000000000000004 y1[1] (closed_form) 0.9736663950053748 y1[1] (numeric) 0.9741064979173903 absolute error 0.00044010291201557195 relative error 0.04520058556741527% Desired digits 8 Estimated correct digits 13 Correct digits 4 h 0.001 y2[1] (closed_form) 0.22797752353518844 y2[1] (numeric) 0.19866933079506122 absolute error 0.02930819274012722 relative error 12.855737831367172% Desired digits 8 Estimated correct digits 13 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.24000000000000005 y1[1] (closed_form) 0.9713379748520296 y1[1] (numeric) 0.9721198046094399 absolute error 0.0007818297574103683 relative error 0.08048998161834141% Desired digits 8 Estimated correct digits 13 Correct digits 4 h 0.001 y2[1] (closed_form) 0.23770262642713463 y2[1] (numeric) 0.19866933079506122 absolute error 0.03903329563207342 relative error 16.42106198773478% Desired digits 8 Estimated correct digits 13 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.25000000000000006 y1[1] (closed_form) 0.9689124217106447 y1[1] (numeric) 0.9701331113014895 absolute error 0.001220689590844759 relative error 0.1259855445644503% Desired digits 8 Estimated correct digits 13 Correct digits 3 h 0.001 y2[1] (closed_form) 0.247403959254523 y2[1] (numeric) 0.19866933079506122 absolute error 0.048734628459461776 relative error 19.698402809037027% Desired digits 8 Estimated correct digits 13 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.26000000000000006 y1[1] (closed_form) 0.9663899781345132 y1[1] (numeric) 0.9681464179935391 absolute error 0.001756439859025849 relative error 0.1817526980584403% Desired digits 8 Estimated correct digits 13 Correct digits 3 h 0.001 y2[1] (closed_form) 0.2570805518921552 y2[1] (numeric) 0.19866933079506122 absolute error 0.05841122109709396 relative error 22.72098012361408% Desired digits 8 Estimated correct digits 13 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2700000000000001 y1[1] (closed_form) 0.9637708963658905 y1[1] (numeric) 0.9661597246855886 absolute error 0.002388828319698111 relative error 0.24786267449097205% Desired digits 8 Estimated correct digits 13 Correct digits 3 h 0.001 y2[1] (closed_form) 0.2667314366888312 y2[1] (numeric) 0.19866933079506122 absolute error 0.06806210589376999 relative error 25.517091925377816% Desired digits 8 Estimated correct digits 13 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2800000000000001 y1[1] (closed_form) 0.9610554383107709 y1[1] (numeric) 0.9641730313776382 absolute error 0.003117593066867319 relative error 0.3243926356992531% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.2763556485641138 y2[1] (numeric) 0.19866933079506122 absolute error 0.0776863177690526 relative error 28.110993269974568% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2900000000000001 y1[1] (closed_form) 0.9582438755126972 y1[1] (numeric) 0.9621863380696878 absolute error 0.0039424625569906 relative error 0.4114258027353665% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.28595222510483564 y2[1] (numeric) 0.19866933079506122 absolute error 0.08728289430977443 relative error 30.52359333024068% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3000000000000001 y1[1] (closed_form) 0.955336489125606 y1[1] (numeric) 0.9601996447617374 absolute error 0.004863155636131378 relative error 0.5090515950649487% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.29552020666133966 y2[1] (numeric) 0.19866933079506122 absolute error 0.09685087586627844 relative error 32.773013040447566% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3100000000000001 y1[1] (closed_form) 0.9523335698857134 y1[1] (numeric) 0.9582129514537869 absolute error 0.0058793815680735495 relative error 0.6173657795953907% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.3050586364434436 y2[1] (numeric) 0.19866933079506122 absolute error 0.10638930564838239 relative error 34.87503480928541% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3200000000000001 y1[1] (closed_form) 0.9492354180824408 y1[1] (numeric) 0.9562262581458365 absolute error 0.006990840063395676 relative error 0.7364706299642649% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.3145665606161179 y2[1] (numeric) 0.19866933079506122 absolute error 0.11589722982105666 relative error 36.84346791154707% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3300000000000001 y1[1] (closed_form) 0.9460423435283869 y1[1] (numeric) 0.9542395648378861 absolute error 0.00819722130949918 relative error 0.8664750965508148% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.3240430283948685 y2[1] (numeric) 0.19866933079506122 absolute error 0.12537369759980727 relative error 38.69044744484701% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.34000000000000014 y1[1] (closed_form) 0.9427546655283462 y1[1] (numeric) 0.9522528715299357 absolute error 0.00949820600158946 relative error 1.0074949877088542% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.3334870921408145 y2[1] (numeric) 0.19866933079506122 absolute error 0.1348177613457533 relative error 40.42668052916023% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.35000000000000014 y1[1] (closed_form) 0.9393727128473789 y1[1] (numeric) 0.9502661782219852 absolute error 0.010893465374606337 relative error 1.1596531627565183% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.3428978074554515 y2[1] (numeric) 0.19866933079506122 absolute error 0.1442284766603903 relative error 42.06165030061562% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.36000000000000015 y1[1] (closed_form) 0.9358968236779348 y1[1] (numeric) 0.9482794849140348 absolute error 0.01238266123609999 relative error 1.3230797372981757% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.3522742332750901 y2[1] (numeric) 0.19866933079506122 absolute error 0.1536049024800289 relative error 43.60378590621449% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.37000000000000016 y1[1] (closed_form) 0.9323273456060344 y1[1] (numeric) 0.9462927916060844 absolute error 0.013965446000050008 relative error 1.4979123014966536% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.36161543196496215 y2[1] (numeric) 0.19866933079506122 absolute error 0.16294610116990094 relative error 45.060604931730126% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.38000000000000017 y1[1] (closed_form) 0.9286646355765101 y1[1] (numeric) 0.944306098298134 absolute error 0.01564146272162381 relative error 1.6842961519594932% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.37092046941298285 y2[1] (numeric) 0.19866933079506122 absolute error 0.17225113861792163 relative error 46.438833340884514% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3900000000000002 y1[1] (closed_form) 0.924909059857313 y1[1] (numeric) 0.9423194049901835 absolute error 0.01741034513287054 relative error 1.8823845379519215% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.3801884151231616 y2[1] (numeric) 0.19866933079506122 absolute error 0.18151908432810038 relative error 47.74450696223805% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4000000000000002 y1[1] (closed_form) 0.921060994002885 y1[1] (numeric) 0.9403327116822331 absolute error 0.0192717176793481 relative error 2.0923389227019786% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.3894183423086507 y2[1] (numeric) 0.19866933079506122 absolute error 0.19074901151358947 relative error 48.98305775294039% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4100000000000002 y1[1] (closed_form) 0.917120822816605 y1[1] (numeric) 0.9383460183742827 absolute error 0.021225195557677656 relative error 2.3143292606193526% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.39860932798442306 y2[1] (numeric) 0.19866933079506122 absolute error 0.19993999718936184 relative error 50.15938743841317% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4200000000000002 y1[1] (closed_form) 0.9130889403123081 y1[1] (numeric) 0.9363593250663322 absolute error 0.023270384754024098 relative error 2.5485342913106384% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.40776045305957037 y2[1] (numeric) 0.19866933079506122 absolute error 0.20909112226450915 relative error 51.27793063197394% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4300000000000002 y1[1] (closed_form) 0.9089657496748851 y1[1] (numeric) 0.9343726317583818 absolute error 0.02540688208349673 relative error 2.7951418513386397% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.416870802429211 y2[1] (numeric) 0.19866933079506122 absolute error 0.21820147163414977 relative error 52.342709146967096% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4400000000000002 y1[1] (closed_form) 0.9047516632199634 y1[1] (numeric) 0.9323859384504314 absolute error 0.02763427523046802 relative error 3.0543492047441054% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.4259394650659998 y2[1] (numeric) 0.19866933079506122 absolute error 0.22727013427093856 relative error 53.3573789025919% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.45000000000000023 y1[1] (closed_form) 0.9004471023526768 y1[1] (numeric) 0.930399245142481 absolute error 0.02995214278980418 relative error 3.3263633934237338% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.4349655341112304 y2[1] (numeric) 0.19866933079506122 absolute error 0.23629620331616918 relative error 54.32527057551714% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.46000000000000024 y1[1] (closed_form) 0.8960524975255252 y1[1] (numeric) 0.9284125518345305 absolute error 0.03236005430900535 relative error 3.6114016085406346% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.44394810696552 y2[1] (numeric) 0.19866933079506122 absolute error 0.2452787761704588 relative error 55.24942494900846% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.47000000000000025 y1[1] (closed_form) 0.8915682881953289 y1[1] (numeric) 0.9264258585265801 absolute error 0.03485757033125125 relative error 3.9096915842316835% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.4528862853790685 y2[1] (numeric) 0.19866933079506122 absolute error 0.2542169545840073 relative error 56.13262374929861% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.48000000000000026 y1[1] (closed_form) 0.886994922779284 y1[1] (numeric) 0.9244391652186297 absolute error 0.03744424243934563 relative error 4.22147201497151% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.4617791755414831 y2[1] (numeric) 0.19866933079506122 absolute error 0.2631098447464219 relative error 56.97741662730867% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.49000000000000027 y1[1] (closed_form) 0.8823328586101213 y1[1] (numeric) 0.9224524719106793 absolute error 0.04011961330055791 relative error 4.546992998056946% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.47062588817115825 y2[1] (numeric) 0.19866933079506122 absolute error 0.27195655737609703 relative error 57.7861448363825% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5000000000000002 y1[1] (closed_form) 0.8775825618903726 y1[1] (numeric) 0.9204657786027288 absolute error 0.042883216712356176 relative error 4.886516502787249% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.47942553860420317 y2[1] (numeric) 0.19866933079506122 absolute error 0.28075620780914196 relative error 58.56096206859026% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5100000000000002 y1[1] (closed_form) 0.8727445076457512 y1[1] (numeric) 0.9184790852947784 absolute error 0.04573457764902722 relative error 5.240316868037052% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.4881772468829077 y2[1] (numeric) 0.19866933079506122 absolute error 0.2895079160878465 relative error 59.30385283959921% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5200000000000002 y1[1] (closed_form) 0.8678191796776498 y1[1] (numeric) 0.916492391986828 absolute error 0.048673212309178204 relative error 5.608681330050553% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.4968801378437369 y2[1] (numeric) 0.19866933079506122 absolute error 0.2982108070486757 relative error 60.01664875211002% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5300000000000002 y1[1] (closed_form) 0.8628070705147609 y1[1] (numeric) 0.9145056986788775 absolute error 0.05169862816411663 relative error 5.991910582428656% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.5055333412048472 y2[1] (numeric) 0.19866933079506122 absolute error 0.30686401040978595 relative error 60.70104291804595% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5400000000000003 y1[1] (closed_form) 0.857708681363824 y1[1] (numeric) 0.9125190053709271 absolute error 0.05481032400710306 relative error 6.390319370435933% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.5141359916531133 y2[1] (numeric) 0.19866933079506122 absolute error 0.3154666608580521 relative error 61.35860277817253% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5500000000000003 y1[1] (closed_form) 0.8525245220595056 y1[1] (numeric) 0.9105323120629767 absolute error 0.058007790003471116 relative error 6.804237121923188% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.5226872289306594 y2[1] (numeric) 0.19866933079506122 absolute error 0.3240178981355982 relative error 61.990781523109106% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5600000000000003 y1[1] (closed_form) 0.847255111013416 y1[1] (numeric) 0.9085456187550263 absolute error 0.06129050774161027 relative error 7.234008617345449% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.5311861979208836 y2[1] (numeric) 0.19866933079506122 absolute error 0.3325168671258224 relative error 62.59892829055555% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5700000000000003 y1[1] (closed_form) 0.8419009751622686 y1[1] (numeric) 0.9065589254470758 absolute error 0.06465795028480725 relative error 7.679994701555612% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.5396320487339695 y2[1] (numeric) 0.19866933079506122 absolute error 0.3409627179389083 relative error 63.18429728902142% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5800000000000003 y1[1] (closed_form) 0.8364626499151868 y1[1] (numeric) 0.9045722321391254 absolute error 0.06810958222393859 relative error 8.14257304027198% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.5480239367918738 y2[1] (numeric) 0.19866933079506122 absolute error 0.34935460599681256 relative error 63.7480559776149% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5900000000000003 y1[1] (closed_form) 0.8309406791001633 y1[1] (numeric) 0.902585538831175 absolute error 0.07164485973101165 relative error 8.622138924357008% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.556361022912784 y2[1] (numeric) 0.19866933079506122 absolute error 0.3576916921177228 relative error 64.29129241388196% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6000000000000003 y1[1] (closed_form) 0.8253356149096781 y1[1] (numeric) 0.9005988455232246 absolute error 0.07526323061354645 relative error 9.119106125304311% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.5646424733950356 y2[1] (numeric) 0.19866933079506122 absolute error 0.3659731425999744 relative error 64.81502186675425% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6100000000000003 y1[1] (closed_form) 0.8196480178454794 y1[1] (numeric) 0.8986121522152741 absolute error 0.07896413436979477 relative error 9.633907805616282% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.001 y2[1] (closed_form) 0.5728674601004815 y2[1] (numeric) 0.19866933079506122 absolute error 0.3741981293054203 relative error 65.32019277893451% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6200000000000003 y1[1] (closed_form) 0.8138784566625338 y1[1] (numeric) 0.8966254589073237 absolute error 0.08274700224478992 relative error 10.166997488065974% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.5810351605373053 y2[1] (numeric) 0.19866933079506122 absolute error 0.3823658297422441 relative error 65.80769215216785% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6300000000000003 y1[1] (closed_form) 0.8080275083121516 y1[1] (numeric) 0.8946387655993733 absolute error 0.08661125728722163 relative error 10.718850088178257% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.5891447579422698 y2[1] (numeric) 0.19866933079506122 absolute error 0.3904754271472086 relative error 66.27835041951968% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6400000000000003 y1[1] (closed_form) 0.8020957578842924 y1[1] (numeric) 0.8926520722914228 absolute error 0.09055631440713041 relative error 11.289963014639675% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.5971954413623923 y2[1] (numeric) 0.19866933079506122 absolute error 0.3985261105673311 relative error 66.73294586076655% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6500000000000004 y1[1] (closed_form) 0.7960837985490556 y1[1] (numeric) 0.8906653789834724 absolute error 0.09458158043441678 relative error 11.88085734275731% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.6051864057360399 y2[1] (numeric) 0.19866933079506122 absolute error 0.40651707494097866 relative error 67.17220861009996% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6600000000000004 y1[1] (closed_form) 0.7899922314973649 y1[1] (numeric) 0.888678685675522 absolute error 0.09868645417815713 relative error 12.492079066537798% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.6131168519734341 y2[1] (numeric) 0.19866933079506122 absolute error 0.4144475211783729 relative error 67.59682429938015% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6700000000000004 y1[1] (closed_form) 0.783821665880849 y1[1] (numeric) 0.8866919923675716 absolute error 0.10287032648672256 relative error 13.124200435454686% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.6209859870365599 y2[1] (numeric) 0.19866933079506122 absolute error 0.4223166562414987 relative error 68.00743737501362% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6800000000000004 y1[1] (closed_form) 0.7775727187509277 y1[1] (numeric) 0.8847052990596211 absolute error 0.10713258030869344 relative error 13.777821382518203% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.6287930240184688 y2[1] (numeric) 0.19866933079506122 absolute error 0.4301236932234076 relative error 68.40465412204924% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6900000000000004 y1[1] (closed_form) 0.7712460149971063 y1[1] (numeric) 0.8827186057516707 absolute error 0.1114725907545644 relative error 14.453571050864053% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.6365371822219682 y2[1] (numeric) 0.19866933079506122 absolute error 0.437867851426907 relative error 68.78904542519201% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7000000000000004 y1[1] (closed_form) 0.7648421872844882 y1[1] (numeric) 0.8807319124437203 absolute error 0.11588972515923213 relative error 15.152109426741935% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.6442176872376913 y2[1] (numeric) 0.19866933079506122 absolute error 0.44554835644263013 relative error 69.16114929304014% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7100000000000004 y1[1] (closed_form) 0.7583618759905079 y1[1] (numeric) 0.8787452191357699 absolute error 0.120383343145262 relative error 15.874129087518739% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.651833771021537 y2[1] (numeric) 0.19866933079506122 absolute error 0.45316444022647573 relative error 69.52147316888602% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7200000000000004 y1[1] (closed_form) 0.7518057291408947 y1[1] (numeric) 0.8767585258278194 absolute error 0.12495279668692472 relative error 16.620357074122204% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.6593846719714734 y2[1] (numeric) 0.19866933079506122 absolute error 0.4607153411764122 relative error 69.87049604882897% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7300000000000004 y1[1] (closed_form) 0.7451744023448701 y1[1] (numeric) 0.874771832519869 absolute error 0.12959743017499892 relative error 17.391556898249526% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.6668696350036982 y2[1] (numeric) 0.19866933079506122 absolute error 0.468200304208637 relative error 70.2086704256733% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7400000000000004 y1[1] (closed_form) 0.7384685587295876 y1[1] (numeric) 0.8727851392119186 absolute error 0.13431658048233097 relative error 18.188530695660262% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.6742879116281454 y2[1] (numeric) 0.19866933079506122 absolute error 0.47561858083308417 relative error 70.53642407508814% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7500000000000004 y1[1] (closed_form) 0.7316888688738206 y1[1] (numeric) 0.8707984459039682 absolute error 0.1391095770301476 relative error 19.012121537978047% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.6816387600233345 y2[1] (numeric) 0.19866933079506122 absolute error 0.48296942922827324 relative error 70.85416169874786% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7600000000000005 y1[1] (closed_form) 0.7248360107409049 y1[1] (numeric) 0.8688117525960177 absolute error 0.14397574185511286 relative error 19.863215916652006% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.6889214451105516 y2[1] (numeric) 0.19866933079506122 absolute error 0.49025211431549043 relative error 71.16226643762256% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7700000000000005 y1[1] (closed_form) 0.7179106696109431 y1[1] (numeric) 0.8668250592880673 absolute error 0.14891438967712423 relative error 20.742746414094295% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.696135238627357 y2[1] (numeric) 0.19866933079506122 absolute error 0.49746590783229583 relative error 71.46110126721952% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7800000000000005 y1[1] (closed_form) 0.7109135380122771 y1[1] (numeric) 0.8648383659801169 absolute error 0.1539248279678398 relative error 21.65169457852997% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.7032794192004105 y2[1] (numeric) 0.19866933079506122 absolute error 0.5046100884053493 relative error 71.75101028536608% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7900000000000005 y1[1] (closed_form) 0.7038453156522357 y1[1] (numeric) 0.8628516726721664 absolute error 0.1590063570199307 relative error 22.591094020791132% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 y2[1] (closed_form) 0.7103532724176082 y2[1] (numeric) 0.19866933079506122 absolute error 0.5116839416225469 relative error 72.03231990205207% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.001 Finished! diff ( y1 , x , 1 ) = neg ( y2 ) ; diff ( y2 , x , 1 ) = y1 ; Iterations 600 Total Elapsed Time 3 Seconds Elapsed Time(since restart) 3 Seconds Time to Timeout 2 Minutes 57.0 Seconds Percent Done 100.16666666666673%