Initializing... Initialized Initializing(2)... PI = 0.3141592653589793238462643383279486e1+/-0.313e-31 E = 0.2718281828459045235360287471352649e1+/-0.256e-30 LOG_E_10 = 0.2302585092994045684017991454684277e1+/-0.5e-30 Initialized(2) ##############ECHO OF PROBLEM################# ##############temp/lin_coshpostode.ode################# diff ( y , x , 1 ) = cosh ( 2.0 * x + 3.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.1) x_end=c(2.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_min_h=c(0.000000001) # 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=(20.0) $glob_subiter_method=3 $glob_max_iter=1000 $glob_upper_ratio_limit=c(1.11) $glob_lower_ratio_limit=c(0.99) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(sinh(c(2.0)*c(x)+c(3.0))/c(2)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1e0+/-0.50e-31 y[1] (closed_form) 0.61229419982827456070985461164548e1+/-0.402e-29 y[1] (numeric) 0.61229419982827456070985461164548e1+/-0.462e-29 absolute error 0.0e0+/-0.864e-29 relative error 0.0e0+/-0.1411086370314008244433002691422749e-27% Desired digits 8 Estimated correct digits 14 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.2e0+/-0.5e-31 y[1] (closed_form) 0.748268169435917181717008822556465e1+/-0.507e-29 y[1] (numeric) 0.748268169383965386859675431701524e1+/-0.831e-29 absolute error 0.51951794857333390854941e-9+/-0.133e-28 relative error 0.6942937970553700156840858800665345e-8+/-0.177e-27% Desired digits 8 Estimated correct digits 13 Correct digits 11 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.3e0+/-0.5e-31 y[1] (closed_form) 0.914272768030767379794830070918684e1+/-0.632e-29 y[1] (numeric) 0.9142727679153921491668685798853796e1+/-0.11e-28 absolute error 0.1153752306279614910333044e-8+/-0.173e-28 relative error 0.1261934453942730244058200498392475e-7+/-0.189e-27% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.4e0+/-0.5e-31 y[1] (closed_form) 0.1116970343036116436044481135163089e2+/-0.792e-29 y[1] (numeric) 0.1116970342843300723560334139713871e2+/-0.15e-28 absolute error 0.192815712484146995449218e-8+/-0.229e-28 relative error 0.1726238424200600619569908412412663e-7+/-0.205e-27% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.5e0+/-0.5e-31 y[1] (closed_form) 0.1364495859856387622445413579539663e2+/-0.105e-28 y[1] (numeric) 0.1364495859569006423570660572248348e2+/-0.18e-28 absolute error 0.287381198874753007291315e-8+/-0.285e-28 relative error 0.2106134634259716313971994875101221e-7+/-0.208e-27% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.6e0+/-0.5e-31 y[1] (closed_form) 0.1666783386602616598470243757344036e2+/-0.133e-28 y[1] (numeric) 0.1666783386199749663659665563466909e2+/-0.24e-28 absolute error 0.402866934810578193877127e-8+/-0.373e-28 relative error 0.2417032339347566626177700268532441e-7+/-0.223e-27% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.7e0+/-0.5e-31 y[1] (closed_form) 0.2035964783126626225080546808498558e2+/-0.167e-28 y[1] (numeric) 0.2035964782582718456707897594388725e2+/-0.302e-28 absolute error 0.543907768372649214109833e-8+/-0.469e-28 relative error 0.2671498902536866876524584223906689e-7+/-0.23e-27% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.8e0+/-0.5e-31 y[1] (closed_form) 0.2486856595154729378845298009830815e2+/-0.208e-28 y[1] (numeric) 0.2486856594438565215405530282130847e2+/-0.42e-28 absolute error 0.716164163439767727699968e-8+/-0.628e-28 relative error 0.2879796787780635219468976987238995e-7+/-0.252e-27% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.9e0+/-0.5e-31 y[1] (closed_form) 0.303755469429214651820516885677787e2+/-0.259e-28 y[1] (numeric) 0.3037554693365597144225965423482013e2+/-0.554e-28 absolute error 0.926549373979203433295857e-8+/-0.813e-28 relative error 0.3050313384382107161582754533062186e-7+/-0.267e-27% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.1e1+/-0.5e-31 y[1] (closed_form) 0.3710160528889437948850473599803132e2+/-0.331e-28 y[1] (numeric) 0.3710160527705931051647991916095222e2+/-0.73e-28 absolute error 0.118350689720248168370791e-7+/-0.106e-27 relative error 0.3189907520138328644130452611759299e-7+/-0.285e-27% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.11e1+/-0.5e-31 y[1] (closed_form) 0.4531668132768260464939153501716992e2+/-0.405e-28 y[1] (numeric) 0.4531668131270911124183541960582305e2+/-0.879e-28 absolute error 0.1497349340755611541134687e-7+/-0.128e-27 relative error 0.3304190194176742666318720134814441e-7+/-0.282e-27% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.12e1+/-0.5e-31 y[1] (closed_form) 0.553504749058111185892782577738915e2+/-0.528e-28 y[1] (numeric) 0.5535047488700439555053884246456347e2+/-0.109e-27 absolute error 0.1880672303873941530932803e-7+/-0.161e-27 relative error 0.3397752787260175950350530380520558e-7+/-0.29e-27% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.13e1+/-0.5e-31 y[1] (closed_form) 0.6760567739060903630552508847375925e2+/-0.645e-28 y[1] (numeric) 0.6760567736712043747546886090850877e2+/-0.128e-27 absolute error 0.2348859883005622756525048e-7+/-0.192e-27 relative error 0.3474353003571705925556431935998477e-7+/-0.283e-27% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.14e1+/-0.5e-31 y[1] (closed_form) 0.825741330887258195763742591800526e2+/-0.795e-28 y[1] (numeric) 0.8257413305951879868018126336757764e2+/-0.15e-27 absolute error 0.2920702089619299581247496e-7+/-0.229e-27 relative error 0.3537066609565259671510502628454879e-7+/-0.277e-27% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.15e1+/-0.5e-31 y[1] (closed_form) 0.1008565786851396140624910338439862e3+/-0.107e-27 y[1] (numeric) 0.1008565786489481244690855191830299e3+/-0.178e-27 absolute error 0.361914895934055146609563e-7+/-0.285e-27 relative error 0.3588411392219676045787791977500569e-7+/-0.282e-27% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.16e1+/-0.5e-31 y[1] (closed_form) 0.1231867529156549897089246762032276e3+/-0.133e-27 y[1] (numeric) 0.1231867528709326735342787947559006e3+/-0.218e-27 absolute error 0.44722316174645881447327e-7+/-0.351e-27 relative error 0.3630448495161399620289343723865425e-7+/-0.284e-27% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.17e1+/-0.5e-31 y[1] (closed_form) 0.1504608440787022206686997982156958e3+/-0.166e-27 y[1] (numeric) 0.1504608440235603480043167686005194e3+/-0.28e-27 absolute error 0.551418726643830296151764e-7+/-0.446e-27 relative error 0.3664865301137066986681356223825282e-7+/-0.296e-27% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.18e1+/-0.5e-31 y[1] (closed_form) 0.1837734572184838367534212137491123e3+/-0.206e-27 y[1] (numeric) 0.1837734571506155043033268323474269e3+/-0.357e-27 absolute error 0.678683324500943814016854e-7+/-0.563e-27 relative error 0.3693043243421565263898863986284971e-7+/-0.306e-27% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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] 0.19e1+/-0.5e-31 y[1] (closed_form) 0.224461544468817463193691295365559e3+/-0.254e-27 y[1] (numeric) 0.2244615443854050101450796264402985e3+/-0.467e-27 absolute error 0.834124530486116689252605e-7+/-0.721e-27 relative error 0.3716113298872870087424358479425131e-7+/-0.321e-27% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.5e-1+/-0.1e-100 NO POLE (given) for Equation 1 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 ) = cosh ( 2.0 * x + 3.0 ) ; Iterations 38 Total Elapsed Time 1 Minutes 2 Seconds Elapsed Time(since restart) 1 Minutes 2 Seconds Time to Timeout 18 Minutes 58 Seconds Percent Done 0.1026315789473684210526315789473684e3+/-0.157e-28%