##############ECHO OF PROBLEM################# ##############temp/sinh_sqrtpostode.ode################# diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(2.0) x_end=c(3.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true # ELIMINATED in preodein.rb $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 $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(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * cosh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * sinh( 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] 2.0 y[1] (closed_form) 1.7549809219803194 y[1] (numeric) 1.7549809219803194 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] 2.009999999999999 y[1] (closed_form) 1.7617403966622582 y[1] (numeric) 1.7617399198160417 absolute error 4.768462165127829e-07 relative error 2.7066769736120134e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.019999999999998 y[1] (closed_form) 1.7685094039062363 y[1] (numeric) 1.7685084505973405 absolute error 9.53308895823568e-07 relative error 5.390465516993717e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0299999999999967 y[1] (closed_form) 1.7752879360606357 y[1] (numeric) 1.775286506670873 absolute error 1.4293897627748464e-06 relative error 8.051593962535804e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0399999999999956 y[1] (closed_form) 1.7820759855082482 y[1] (numeric) 1.7820740804177186 absolute error 1.9050905295525666e-06 relative error 0.0001069028787237282% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0499999999999945 y[1] (closed_form) 1.788873544666064 y[1] (numeric) 1.7888711642531592 absolute error 2.3804129047899636e-06 relative error 0.00013306770128541% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0599999999999934 y[1] (closed_form) 1.7956806059850514 y[1] (numeric) 1.795677750626464 absolute error 2.8553585873503096e-06 relative error 0.00015901260936011243% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0699999999999923 y[1] (closed_form) 1.8024971619499262 y[1] (numeric) 1.8024938320206765 absolute error 3.329929249673569e-06 relative error 0.0001847397776799426% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.079999999999991 y[1] (closed_form) 1.8093232050789716 y[1] (numeric) 1.8093194009523996 absolute error 3.804126571971267e-06 relative error 0.00021025135593754948% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.08999999999999 y[1] (closed_form) 1.8161587279238063 y[1] (numeric) 1.816154449971588 absolute error 4.277952218245673e-06 relative error 0.0002355494678119977% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.099999999999989 y[1] (closed_form) 1.8230037230691654 y[1] (numeric) 1.8229989716613375 absolute error 4.7514078278521055e-06 relative error 0.00026063621087140456% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.109999999999988 y[1] (closed_form) 1.829858183132746 y[1] (numeric) 1.8298529586376793 absolute error 5.224495066791235e-06 relative error 0.0002855136597442113% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.119999999999987 y[1] (closed_form) 1.8367221007649164 y[1] (numeric) 1.836716403549375 absolute error 5.697215541333733e-06 relative error 0.0003101838617263377% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1299999999999857 y[1] (closed_form) 1.8435954686485942 y[1] (numeric) 1.843589299077714 absolute error 6.169570880176778e-06 relative error 0.000334648841630059% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1399999999999846 y[1] (closed_form) 1.8504782794990149 y[1] (numeric) 1.85047163793631 absolute error 6.641562704912118e-06 relative error 0.00035891060049136095% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1499999999999835 y[1] (closed_form) 1.8573705260635087 y[1] (numeric) 1.8573634128709031 absolute error 7.113192605601171e-06 relative error 0.00038297111458297957% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1599999999999824 y[1] (closed_form) 1.8642722011213415 y[1] (numeric) 1.8642646166591614 absolute error 7.584462180076912e-06 relative error 0.0004068323378697023% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1699999999999813 y[1] (closed_form) 1.871183297483487 y[1] (numeric) 1.8711752421104846 absolute error 8.055373002413546e-06 relative error 0.00043049620062593757% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.17999999999998 y[1] (closed_form) 1.8781038079924617 y[1] (numeric) 1.8780952820658081 absolute error 8.52592665356866e-06 relative error 0.00045396461139611733% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.189999999999979 y[1] (closed_form) 1.885033725522101 y[1] (numeric) 1.8850247293974118 absolute error 8.996124689186757e-06 relative error 0.0004772394555803019% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.199999999999978 y[1] (closed_form) 1.8919730429773924 y[1] (numeric) 1.8919635770087275 absolute error 9.465968664912339e-06 relative error 0.0005003225970923863% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.209999999999977 y[1] (closed_form) 1.8989217532942746 y[1] (numeric) 1.8989118178341502 absolute error 9.935460124399498e-06 relative error 0.0005232158780193723% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2199999999999758 y[1] (closed_form) 1.9058798494394544 y[1] (numeric) 1.905869444838848 absolute error 1.0404600606417347e-05 relative error 0.0005459211192918317% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2299999999999747 y[1] (closed_form) 1.9128473244102047 y[1] (numeric) 1.9128364510185782 absolute error 1.0873391626420315e-05 relative error 0.0005684401200065953% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2399999999999736 y[1] (closed_form) 1.9198241712342021 y[1] (numeric) 1.9198128293994996 absolute error 1.1341834702527365e-05 relative error 0.0005907746590791183% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2499999999999725 y[1] (closed_form) 1.9268103829693395 y[1] (numeric) 1.9267985730379913 absolute error 1.1809931348194525e-05 relative error 0.0006129264951330943% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2599999999999714 y[1] (closed_form) 1.9338059527035174 y[1] (numeric) 1.9337936750204674 absolute error 1.2277683050010424e-05 relative error 0.0006348973656248117% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2699999999999703 y[1] (closed_form) 1.9408108735545078 y[1] (numeric) 1.9407981284632012 absolute error 1.2745091306554102e-05 relative error 0.000656688989134322% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.279999999999969 y[1] (closed_form) 1.9478251386697352 y[1] (numeric) 1.947811926512142 absolute error 1.3212157593089913e-05 relative error 0.0006783030638013605% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.289999999999968 y[1] (closed_form) 1.954848741226117 y[1] (numeric) 1.9548350623427404 absolute error 1.3678883376666562e-05 relative error 0.0006997412683749084% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.299999999999967 y[1] (closed_form) 1.9618816744298933 y[1] (numeric) 1.9618675291597711 absolute error 1.4145270122112308e-05 relative error 0.0007210052627777772% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.309999999999966 y[1] (closed_form) 1.9689239315164393 y[1] (numeric) 1.968909320197158 absolute error 1.4611319281376822e-05 relative error 0.0007420966878148196% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3199999999999648 y[1] (closed_form) 1.9759755057501103 y[1] (numeric) 1.9759604287178012 absolute error 1.5077032309074312e-05 relative error 0.0007630171662148637% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3299999999999637 y[1] (closed_form) 1.9830363904240293 y[1] (numeric) 1.9830208480134073 absolute error 1.55424106220714e-05 relative error 0.0007837683008302229% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3399999999999626 y[1] (closed_form) 1.990106578859983 y[1] (numeric) 1.9900905714043162 absolute error 1.6007455666766646e-05 relative error 0.0008043516782873202% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3499999999999615 y[1] (closed_form) 1.9971860644081811 y[1] (numeric) 1.9971695922393333 absolute error 1.6472168847814217e-05 relative error 0.0008247688656237122% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3599999999999604 y[1] (closed_form) 2.0042748404471524 y[1] (numeric) 2.0042579038955632 absolute error 1.6936551589186166e-05 relative error 0.0008450214136005236% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3699999999999593 y[1] (closed_form) 2.0113729003835186 y[1] (numeric) 2.0113554997782406 absolute error 1.740060527799514e-05 relative error 0.0008651108541174677% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.379999999999958 y[1] (closed_form) 2.0184802376518913 y[1] (numeric) 2.0184623733205695 absolute error 1.786433132178189e-05 relative error 0.0008850387033049955% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.389999999999957 y[1] (closed_form) 2.025596845714654 y[1] (numeric) 2.025578517983556 absolute error 1.8327731098111144e-05 relative error 0.0009048064592362113% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.399999999999956 y[1] (closed_form) 2.0327227180618372 y[1] (numeric) 2.032703927255848 absolute error 1.8790805989432613e-05 relative error 0.000924415603882722% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.409999999999955 y[1] (closed_form) 2.0398578482109393 y[1] (numeric) 2.039838594653574 absolute error 1.925355736531742e-05 relative error 0.0009438676024510132% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4199999999999537 y[1] (closed_form) 2.0470022297067736 y[1] (numeric) 2.046982513720185 absolute error 1.971598658867535e-05 relative error 0.0009631639039054491% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4299999999999526 y[1] (closed_form) 2.054155856121305 y[1] (numeric) 2.0541356780262916 absolute error 2.0178095013534403e-05 relative error 0.000982305941070852% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4399999999999515 y[1] (closed_form) 2.0613187210534925 y[1] (numeric) 2.0612980811695123 absolute error 2.0639883980155815e-05 relative error 0.0010012951306048996% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4499999999999504 y[1] (closed_form) 2.068490818129149 y[1] (numeric) 2.0684697167743153 absolute error 2.1101354833685804e-05 relative error 0.0010201328741101675% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4599999999999493 y[1] (closed_form) 2.0756721410007746 y[1] (numeric) 2.0756505784918637 absolute error 2.156250891083289e-05 relative error 0.001038820557683866% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4699999999999482 y[1] (closed_form) 2.0828626833473862 y[1] (numeric) 2.0828406599998637 absolute error 2.202334752254842e-05 relative error 0.001057359551286142% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.479999999999947 y[1] (closed_form) 2.0900624388744014 y[1] (numeric) 2.09003995500241 absolute error 2.2483871991330062e-05 relative error 0.0010757512107360152% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.489999999999946 y[1] (closed_form) 2.09727140131346 y[1] (numeric) 2.0972484572298375 absolute error 2.2944083622356004e-05 relative error 0.001093996876512348% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.499999999999945 y[1] (closed_form) 2.1044895644222876 y[1] (numeric) 2.1044661604385717 absolute error 2.3403983715919452e-05 relative error 0.0011120978745429977% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.509999999999944 y[1] (closed_form) 2.111716921984545 y[1] (numeric) 2.111693058410976 absolute error 2.3863573569204988e-05 relative error 0.0011300555164741742% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5199999999999427 y[1] (closed_form) 2.1189534678096766 y[1] (numeric) 2.1189291449552083 absolute error 2.4322854468294963e-05 relative error 0.0011478710994742632% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5299999999999416 y[1] (closed_form) 2.12619919573277 y[1] (numeric) 2.126174413905076 absolute error 2.478182769394266e-05 relative error 0.001165545906690172% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5399999999999405 y[1] (closed_form) 2.133454099614392 y[1] (numeric) 2.133428859119888 absolute error 2.524049450380872e-05 relative error 0.0011830812065922007% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5499999999999394 y[1] (closed_form) 2.14071817334049 y[1] (numeric) 2.14069247448431 absolute error 2.569885617997869e-05 relative error 0.0012004782553827174% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5599999999999383 y[1] (closed_form) 2.147991410822195 y[1] (numeric) 2.1479652539082252 absolute error 2.6156913969899165e-05 relative error 0.001217738294395087% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5699999999999372 y[1] (closed_form) 2.1552738059957157 y[1] (numeric) 2.15524719132659 absolute error 2.6614669125901713e-05 relative error 0.001234862552120425% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.579999999999936 y[1] (closed_form) 2.162565352822183 y[1] (numeric) 2.162538280699294 absolute error 2.7072122888771588e-05 relative error 0.0012518522436069748% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.589999999999935 y[1] (closed_form) 2.1698660452875274 y[1] (numeric) 2.1698385160110227 absolute error 2.7529276504623112e-05 relative error 0.0012687085714074681% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.599999999999934 y[1] (closed_form) 2.1771758774023056 y[1] (numeric) 2.177147891271114 absolute error 2.798613119159299e-05 relative error 0.0012854327242034576% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.609999999999933 y[1] (closed_form) 2.1844948432015965 y[1] (numeric) 2.1844664005134256 absolute error 2.8442688170926544e-05 relative error 0.001302025878405871% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6199999999999317 y[1] (closed_form) 2.1918229367448667 y[1] (numeric) 2.1917940377961966 absolute error 2.8898948670086355e-05 relative error 0.0013184891984479793% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6299999999999306 y[1] (closed_form) 2.1991601521158035 y[1] (numeric) 2.1991307972019145 absolute error 2.9354913889001466e-05 relative error 0.0013348238353973092% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6399999999999295 y[1] (closed_form) 2.206506483422208 y[1] (numeric) 2.206476672837177 absolute error 2.9810585031153636e-05 relative error 0.0013510309285345288% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6499999999999284 y[1] (closed_form) 2.213861924795859 y[1] (numeric) 2.213831658832563 absolute error 3.026596329602782e-05 relative error 0.0013671116051566159% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6599999999999273 y[1] (closed_form) 2.2212264703923648 y[1] (numeric) 2.221195749342497 absolute error 3.072104986756585e-05 relative error 0.0013830669802048228% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.669999999999926 y[1] (closed_form) 2.2286001143910497 y[1] (numeric) 2.228568938545119 absolute error 3.1175845930597745e-05 relative error 0.0013988981571562173% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.679999999999925 y[1] (closed_form) 2.235982850994821 y[1] (numeric) 2.2359512206421566 absolute error 3.163035266462444e-05 relative error 0.0014146062278854973% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.689999999999924 y[1] (closed_form) 2.243374674430026 y[1] (numeric) 2.243342589858793 absolute error 3.2084571232715575e-05 relative error 0.0014301922723125732% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.699999999999923 y[1] (closed_form) 2.250775578946346 y[1] (numeric) 2.2507430404435396 absolute error 3.253850280637849e-05 relative error 0.001445657359656031% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.709999999999922 y[1] (closed_form) 2.2581855588166455 y[1] (numeric) 2.25815256666811 absolute error 3.2992148535360144e-05 relative error 0.0014610025472241964% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7199999999999207 y[1] (closed_form) 2.2656046083368633 y[1] (numeric) 2.2655711628272925 absolute error 3.344550957073977e-05 relative error 0.0014762288815828052% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7299999999999196 y[1] (closed_form) 2.2730327218258832 y[1] (numeric) 2.272998823238824 absolute error 3.3898587059155716e-05 relative error 0.0014913373984306586% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7399999999999185 y[1] (closed_form) 2.280469893625405 y[1] (numeric) 2.2804355422432665 absolute error 3.435138213836453e-05 relative error 0.001506329122536847% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7499999999999174 y[1] (closed_form) 2.287916118099833 y[1] (numeric) 2.2878813142038865 absolute error 3.4803895946566854e-05 relative error 0.0015212050682816244% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7599999999999163 y[1] (closed_form) 2.2953713896361236 y[1] (numeric) 2.295336133506526 absolute error 3.525612959753843e-05 relative error 0.0015359662386977581% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.769999999999915 y[1] (closed_form) 2.3028357026437014 y[1] (numeric) 2.3027999945594875 absolute error 3.5708084213936786e-05 relative error 0.0015506136270574229% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.779999999999914 y[1] (closed_form) 2.310309051554327 y[1] (numeric) 2.310272891793409 absolute error 3.615976091841944e-05 relative error 0.0015651482166029653% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.789999999999913 y[1] (closed_form) 2.317791430821954 y[1] (numeric) 2.3177548196611446 absolute error 3.6611160809219e-05 relative error 0.001579570979612935% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.799999999999912 y[1] (closed_form) 2.3252828349226426 y[1] (numeric) 2.3252457726376488 absolute error 3.706228499389397e-05 relative error 0.0015938828789886523% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.809999999999911 y[1] (closed_form) 2.332783258354425 y[1] (numeric) 2.332745745219856 absolute error 3.75131345689006e-05 relative error 0.0016080848674884113% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8199999999999097 y[1] (closed_form) 2.340292695637187 y[1] (numeric) 2.3402547319265627 absolute error 3.796371062403381e-05 relative error 0.0016221778880396627% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8299999999999086 y[1] (closed_form) 2.3478111413125493 y[1] (numeric) 2.3477727272983118 absolute error 3.8414014237542204e-05 relative error 0.0016361628736486344% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8399999999999075 y[1] (closed_form) 2.355338589943777 y[1] (numeric) 2.355299725897278 absolute error 3.8864046499220706e-05 relative error 0.00165004074850013% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8499999999999064 y[1] (closed_form) 2.3628750361156285 y[1] (numeric) 2.3628357223071528 absolute error 3.9313808475771594e-05 relative error 0.0016638124265936742% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8599999999999053 y[1] (closed_form) 2.3704204744342547 y[1] (numeric) 2.37038071113303 absolute error 3.976330122457128e-05 relative error 0.0016774788124483077% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.869999999999904 y[1] (closed_form) 2.3779748995271213 y[1] (numeric) 2.3779346870012934 absolute error 4.0212525827865164e-05 relative error 0.001691040802653625% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.879999999999903 y[1] (closed_form) 2.385538306042829 y[1] (numeric) 2.385497644559504 absolute error 4.0661483324822e-05 relative error 0.0017044992831103164% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.889999999999902 y[1] (closed_form) 2.3931106886510634 y[1] (numeric) 2.39306957847629 absolute error 4.111017477326229e-05 relative error 0.0017178551317421538% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.899999999999901 y[1] (closed_form) 2.400692042042458 y[1] (numeric) 2.4006504834412357 absolute error 4.1558601222124736e-05 relative error 0.001731109217439133% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9099999999998998 y[1] (closed_form) 2.4082823609284745 y[1] (numeric) 2.4082403541647714 absolute error 4.200676370302858e-05 relative error 0.0017442623998140132% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9199999999998987 y[1] (closed_form) 2.4158816400413166 y[1] (numeric) 2.4158391853780636 absolute error 4.245466325292213e-05 relative error 0.0017573155302507315% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9299999999998976 y[1] (closed_form) 2.4234898741338142 y[1] (numeric) 2.423446971832911 absolute error 4.290230090342462e-05 relative error 0.001770269451559332% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9399999999998965 y[1] (closed_form) 2.431107057979302 y[1] (numeric) 2.4310637083016298 absolute error 4.334967767238851e-05 relative error 0.001783124997729227% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9499999999998954 y[1] (closed_form) 2.4387331863715396 y[1] (numeric) 2.4386893895769552 absolute error 4.3796794584327614e-05 relative error 0.0017958829948712231% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9599999999998943 y[1] (closed_form) 2.4463682541245806 y[1] (numeric) 2.4463240104719315 absolute error 4.4243652649100795e-05 relative error 0.0018085442604360946% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.969999999999893 y[1] (closed_form) 2.4540122560726765 y[1] (numeric) 2.4539675658198052 absolute error 4.4690252871237846e-05 relative error 0.0018211096036968744% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.979999999999892 y[1] (closed_form) 2.461665187070185 y[1] (numeric) 2.461620050473926 absolute error 4.513659625926536e-05 relative error 0.0018335798262226657% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.989999999999891 y[1] (closed_form) 2.4693270419914413 y[1] (numeric) 2.4692814593076378 absolute error 4.558268380350228e-05 relative error 0.0018459557210672732% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.99999999999989 y[1] (closed_form) 2.476997815730684 y[1] (numeric) 2.4769517872141797 absolute error 4.60285165040375e-05 relative error 0.001858238073999256% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 Finished! diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 1001 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.19999999998896%