##############ECHO OF PROBLEM################# ##############temp/div_c_linpostode.ode################# diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(2.5) x_end=c(3.1) $array_y_init[0 + 1] = exact_soln_y(x_start) $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 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(-1.5) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(1.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=c(0.0) #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) * ln(c(0.2) * c(x) + c(0.3))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 2.5 y[1] (closed_form) -2.231435513142097 y[1] (numeric) -2.231435513142097 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] 2.509999999999999 y[1] (closed_form) -2.206466711156228 y[1] (numeric) -2.206466711156225 absolute error 3.1086244689504383e-15 relative error 1.4088698702014242e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.519999999999998 y[1] (closed_form) -2.181560098031712 y[1] (numeric) -2.1815600980317065 absolute error 5.329070518200751e-15 relative error 2.4427796066717787e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5299999999999967 y[1] (closed_form) -2.156715364755095 y[1] (numeric) -2.1567153647550876 absolute error 7.549516567451064e-15 relative error 3.5004695987355506e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5399999999999956 y[1] (closed_form) -2.131932204610427 y[1] (numeric) -2.131932204610417 absolute error 1.021405182655144e-14 relative error 4.790983411415691e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5499999999999945 y[1] (closed_form) -2.107210313156539 y[1] (numeric) -2.107210313156526 absolute error 1.3322676295501878e-14 relative error 6.322423638647108e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5599999999999934 y[1] (closed_form) -2.082549388204607 y[1] (numeric) -2.0825493882045913 absolute error 1.554312234475219e-14 relative error 7.463507195933596e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5699999999999923 y[1] (closed_form) -2.0579491297959858 y[1] (numeric) -2.0579491297959684 absolute error 1.7319479184152442e-14 relative error 8.415892761095317e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.579999999999991 y[1] (closed_form) -2.033409240180321 y[1] (numeric) -2.0334092401803012 absolute error 1.9984014443252818e-14 relative error 9.82783693924822e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.58999999999999 y[1] (closed_form) -2.0089294237939237 y[1] (numeric) -2.0089294237939 absolute error 2.353672812205332e-14 relative error 1.171605524976756e-12% Desired digits 8 Estimated correct digits 13 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.599999999999989 y[1] (closed_form) -1.984509387238409 y[1] (numeric) -1.9845093872383825 absolute error 2.6423307986078726e-14 relative error 1.3314781051677818e-12% Desired digits 8 Estimated correct digits 13 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.609999999999988 y[1] (closed_form) -1.9601488392596003 y[1] (numeric) -1.9601488392595712 absolute error 2.90878432451791e-14 relative error 1.4839609453415969e-12% Desired digits 8 Estimated correct digits 13 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.619999999999987 y[1] (closed_form) -1.9358474907266852 y[1] (numeric) -1.9358474907266536 absolute error 3.1530333899354446e-14 relative error 1.628761255749464e-12% Desired digits 8 Estimated correct digits 13 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6299999999999857 y[1] (closed_form) -1.9116050546116239 y[1] (numeric) -1.9116050546115901 absolute error 3.375077994860476e-14 relative error 1.7655728555008358e-12% Desired digits 8 Estimated correct digits 13 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6399999999999846 y[1] (closed_form) -1.8874212459688102 y[1] (numeric) -1.887421245968774 absolute error 3.6193270602780103e-14 relative error 1.917604280447853e-12% Desired digits 8 Estimated correct digits 13 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6499999999999835 y[1] (closed_form) -1.8632957819149736 y[1] (numeric) -1.8632957819149347 absolute error 3.885780586188048e-14 relative error 2.0854341129858065e-12% Desired digits 8 Estimated correct digits 13 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6599999999999824 y[1] (closed_form) -1.8392283816093262 y[1] (numeric) -1.8392283816092845 absolute error 4.1744385725905886e-14 relative error 2.269668418740881e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6699999999999813 y[1] (closed_form) -1.8152187662339472 y[1] (numeric) -1.8152187662339023 absolute error 4.4853010194856324e-14 relative error 2.470942402601606e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.67999999999998 y[1] (closed_form) -1.791266658974401 y[1] (numeric) -1.7912666589743538 absolute error 4.729550084903167e-14 relative error 2.640338366824231e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.689999999999979 y[1] (closed_form) -1.7673717850005897 y[1] (numeric) -1.7673717850005397 absolute error 4.9960036108132044e-14 relative error 2.8267983302740897e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.699999999999978 y[1] (closed_form) -1.7435338714478292 y[1] (numeric) -1.7435338714477768 absolute error 5.240252676230739e-14 relative error 3.005535345223455e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.709999999999977 y[1] (closed_form) -1.7197526473981575 y[1] (numeric) -1.7197526473981024 absolute error 5.5067062021407764e-14 relative error 3.202033856713036e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7199999999999758 y[1] (closed_form) -1.6960278438618561 y[1] (numeric) -1.6960278438617982 absolute error 5.795364188543317e-14 relative error 3.417021842841489e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7299999999999747 y[1] (closed_form) -1.6723591937591973 y[1] (numeric) -1.6723591937591364 absolute error 6.084022174945858e-14 relative error 3.637987698844735e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7399999999999736 y[1] (closed_form) -1.6487464319024017 y[1] (numeric) -1.6487464319023386 absolute error 6.306066779870889e-14 relative error 3.824764474301031e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7499999999999725 y[1] (closed_form) -1.6251892949778135 y[1] (numeric) -1.6251892949777476 absolute error 6.59472476627343e-14 relative error 4.057819471647122e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7599999999999714 y[1] (closed_form) -1.60168752152828 y[1] (numeric) -1.6016875215282118 absolute error 6.816769371198461e-14 relative error 4.255992058110133e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7699999999999703 y[1] (closed_form) -1.5782408519357412 y[1] (numeric) -1.57824085193567 absolute error 7.105427357601002e-14 relative error 4.502118513081236e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.779999999999969 y[1] (closed_form) -1.5548490284040213 y[1] (numeric) -1.5548490284039478 absolute error 7.349676423018536e-14 relative error 4.726938943109242e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.789999999999968 y[1] (closed_form) -1.5315117949418218 y[1] (numeric) -1.5315117949417458 absolute error 7.593925488436071e-14 relative error 4.958450541169057e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.799999999999967 y[1] (closed_form) -1.5082288973459126 y[1] (numeric) -1.508228897345834 absolute error 7.860379014346108e-14 relative error 5.2116618559545666e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.809999999999966 y[1] (closed_form) -1.4850000831845183 y[1] (numeric) -1.4850000831844372 absolute error 8.104628079763643e-14 relative error 5.457661700855679e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8199999999999648 y[1] (closed_form) -1.4618251017808954 y[1] (numeric) -1.461825101780812 absolute error 8.348877145181177e-14 relative error 5.711269518501224e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8299999999999637 y[1] (closed_form) -1.4387037041971023 y[1] (numeric) -1.4387037041970163 absolute error 8.593126210598712e-14 relative error 5.972825527264684e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8399999999999626 y[1] (closed_form) -1.4156356432179544 y[1] (numeric) -1.415635643217866 absolute error 8.837375276016246e-14 relative error 6.2426905668520414e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8499999999999615 y[1] (closed_form) -1.3926206733351645 y[1] (numeric) -1.3926206733350734 absolute error 9.103828801926284e-14 relative error 6.537192055409943e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8599999999999604 y[1] (closed_form) -1.3696585507316648 y[1] (numeric) -1.369658550731571 absolute error 9.370282327836321e-14 relative error 6.841327221905608e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8699999999999593 y[1] (closed_form) -1.3467490332661085 y[1] (numeric) -1.3467490332660121 absolute error 9.636735853746359e-14 relative error 7.155554313171135e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.879999999999958 y[1] (closed_form) -1.323891880457551 y[1] (numeric) -1.3238918804574522 absolute error 9.880984919163893e-14 relative error 7.463589032473649e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.889999999999957 y[1] (closed_form) -1.3010868534703013 y[1] (numeric) -1.3010868534701996 absolute error 1.0169642905566434e-13 relative error 7.81626751391856e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.899999999999956 y[1] (closed_form) -1.2783337150989484 y[1] (numeric) -1.2783337150988445 absolute error 1.0391687510491465e-13 relative error 8.129088193286918e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.909999999999955 y[1] (closed_form) -1.2556322297535594 y[1] (numeric) -1.255632229753453 absolute error 1.0635936575909e-13 relative error 8.4705826466373e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9199999999999537 y[1] (closed_form) -1.2329821634450404 y[1] (numeric) -1.2329821634449314 absolute error 1.0902390101819037e-13 relative error 8.842293445151695e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9299999999999526 y[1] (closed_form) -1.2103832837706674 y[1] (numeric) -1.210383283770556 absolute error 1.1146639167236572e-13 relative error 9.209181353291506e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9399999999999515 y[1] (closed_form) -1.1878353598997784 y[1] (numeric) -1.1878353598996645 absolute error 1.1390888232654106e-13 relative error 9.589618744482562e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9499999999999504 y[1] (closed_form) -1.1653381625596262 y[1] (numeric) -1.1653381625595098 absolute error 1.163513729807164e-13 relative error 9.98434417741495e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9599999999999493 y[1] (closed_form) -1.1428914640213899 y[1] (numeric) -1.1428914640212706 absolute error 1.192379528447418e-13 relative error 1.0433007560069606e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9699999999999482 y[1] (closed_form) -1.1204950380863445 y[1] (numeric) -1.1204950380862229 absolute error 1.2168044349891716e-13 relative error 1.0859525420722171e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.979999999999947 y[1] (closed_form) -1.0981486600721833 y[1] (numeric) -1.0981486600720591 absolute error 1.241229341530925e-13 relative error 1.1302926340130824e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.989999999999946 y[1] (closed_form) -1.0758521067994942 y[1] (numeric) -1.0758521067993674 absolute error 1.2678746941219288e-13 relative error 1.1784841857991748e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.999999999999945 y[1] (closed_form) -1.053605156578385 y[1] (numeric) -1.0536051565782552 absolute error 1.2989609388114332e-13 relative error 1.232872609536051e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.009999999999944 y[1] (closed_form) -1.031407589195258 y[1] (numeric) -1.0314075891951258 absolute error 1.3233858453531866e-13 relative error 1.2830871705973587e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0199999999999427 y[1] (closed_form) -1.0092591858997317 y[1] (numeric) -1.0092591858995967 absolute error 1.3500311979441904e-13 relative error 1.3376456878523905e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0299999999999416 y[1] (closed_form) -0.9871597293917056 y[1] (numeric) -0.9871597293915682 absolute error 1.3744561044859438e-13 relative error 1.3923340504711359e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0399999999999405 y[1] (closed_form) -0.9651090038085681 y[1] (numeric) -0.9651090038084283 absolute error 1.397770788003072e-13 relative error 1.4483035413482927e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0499999999999394 y[1] (closed_form) -0.9431067947125459 y[1] (numeric) -0.9431067947124038 absolute error 1.4210854715202004e-13 relative error 1.506812886395692e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0599999999999383 y[1] (closed_form) -0.9211528890781915 y[1] (numeric) -0.9211528890780469 absolute error 1.4455103780619538e-13 relative error 1.569240454218727e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0699999999999372 y[1] (closed_form) -0.8992470752800074 y[1] (numeric) -0.8992470752798605 absolute error 1.468825061579082e-13 relative error 1.6333943161524542e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.079999999999936 y[1] (closed_form) -0.8773891430802068 y[1] (numeric) -0.8773891430800574 absolute error 1.4932499681208355e-13 relative error 1.7019243740338027e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.089999999999935 y[1] (closed_form) -0.8555788836166069 y[1] (numeric) -0.8555788836164554 absolute error 1.5154544286133387e-13 relative error 1.771262074874242e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.099999999999934 y[1] (closed_form) -0.8338160893906538 y[1] (numeric) -0.8338160893904998 absolute error 1.539879335155092e-13 relative error 1.8467853460112815e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 Finished! diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; Iterations 601 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.33333333332226%