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_sinhpostode.ode################# diff ( y , x , 1 ) = sinh ( 2.0 * x + 3.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #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=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(cosh(c(2.0)*c(x)+c(3.0))/c(2.0)) 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) 0.614332310027192871468158574752701e1+/-0.402e-29 y[1] (numeric) 0.614332310027192871468158574752701e1+/-0.462e-29 absolute error 0.0e0+/-0.864e-29 relative error 0.0e0+/-0.1406404947123415682044609701074437e-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) 0.749936832933933485691128829130012e1+/-0.507e-29 y[1] (numeric) 0.7499368328821338233838791152290915e1+/-0.831e-29 absolute error 0.517996623072497139009205e-9+/-0.133e-28 relative error 0.6907203384663340360746348296894658e-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) 0.9156389541531320078349082240404615e1+/-0.61e-29 y[1] (numeric) 0.915638954038033465354328092585771e1+/-0.11e-28 absolute error 0.1150985424805801314546905e-8+/-0.171e-28 relative error 0.1257029770943220292279215219993758e-7+/-0.186e-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) 0.1118088881628924715833410301290131e2+/-0.792e-29 y[1] (numeric) 0.11180888814364876689946202749569e2+/-0.14e-28 absolute error 0.192437046838790026333231e-8+/-0.219e-28 relative error 0.1721124769244031465260286076278909e-7+/-0.195e-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) 0.1365411641800824331460099480603325e2+/-0.105e-28 y[1] (numeric) 0.1365411641513905290344418021595e2+/-0.186e-28 absolute error 0.286919041115681459008325e-8+/-0.291e-28 relative error 0.210133729881830746203877401716234e-7+/-0.213e-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) 0.1667533165443640483780842975355472e2+/-0.133e-28 y[1] (numeric) 0.1667533165041304064290473939660025e2+/-0.237e-28 absolute error 0.402336419490369035695447e-8+/-0.370e-28 relative error 0.2412764122645375100731513568569982e-7+/-0.221e-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) 0.2036578650121779647139493777810385e2+/-0.167e-28 y[1] (numeric) 0.2036578649578458360524562491420877e2+/-0.327e-28 absolute error 0.543321286614931286389508e-8+/-0.494e-28 relative error 0.2667813917142079156349639091864393e-7+/-0.242e-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) 0.2487359186941961057927404664547393e2+/-0.208e-28 y[1] (numeric) 0.2487359186226429197688883511263049e2+/-0.446e-28 absolute error 0.715531860238521153284344e-8+/-0.654e-28 relative error 0.2876672834365425559601329733588323e-7+/-0.262e-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) 0.3037966181644597519647236958116172e2+/-0.259e-28 y[1] (numeric) 0.3037966180718717964294247428363188e2+/-0.604e-28 absolute error 0.925879555352989529752984e-8+/-0.863e-28 relative error 0.3047695398807126616535060606809979e-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] 0.1e1+/-0.5e-31 y[1] (closed_form) 0.371049742623939222220530540222429e2+/-0.34e-28 y[1] (numeric) 0.3710497425056585858661173163958568e2+/-0.797e-28 absolute error 0.1182806363544132238265722e-7+/-0.113e-27 relative error 0.3187729912382428003641382144596908e-7+/-0.304e-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) 0.453194396098929850356005318945036e2+/-0.427e-28 y[1] (numeric) 0.4531943959492674843804182240390445e2+/-0.101e-27 absolute error 0.1496623659755870949059915e-7+/-0.143e-27 relative error 0.3302387833209584116090875472764589e-7+/-0.315e-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) 0.553527331962824249232690822832444e2+/-0.528e-28 y[1] (numeric) 0.5535273317748316458354462372052864e2+/-0.12e-27 absolute error 0.1879926033972445856271576e-7+/-0.172e-27 relative error 0.3396265957285564704579250784301344e-7+/-0.31e-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) 0.6760752632246727777093543479197985e2+/-0.645e-28 y[1] (numeric) 0.6760752629898631020756455384682578e2+/-0.139e-27 absolute error 0.2348096756337088094515407e-7+/-0.203e-27 relative error 0.3473129226970060733827649069056003e-7+/-0.3e-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) 0.825756468660985074837483552023503e2+/-0.795e-28 y[1] (numeric) 0.8257564683689925586577642891211324e2+/-0.161e-27 absolute error 0.2919925161797192629023706e-7+/-0.24e-27 relative error 0.3536060900052083092339617508886052e-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] 0.15e1+/-0.5e-31 y[1] (closed_form) 0.1008578180612279472417025564277017e3+/-0.107e-27 y[1] (numeric) 0.1008578180250443399208066871494489e3+/-0.189e-27 absolute error 0.361836073208958692782528e-7+/-0.296e-27 relative error 0.3587585773363629384942048175833857e-7+/-0.293e-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) 0.1231877676309731375761063693299575e3+/-0.133e-27 y[1] (numeric) 0.1231877675862587961858691124903754e3+/-0.231e-27 absolute error 0.447143413902372568395821e-7+/-0.364e-27 relative error 0.3629771222430587864258744864509817e-7+/-0.295e-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) 0.1504616748573388076359493398427827e3+/-0.166e-27 y[1] (numeric) 0.1504616748022049854983116547704504e3+/-0.294e-27 absolute error 0.551338221376376850723323e-7+/-0.460e-27 relative error 0.3664310010500226625901993481493701e-7+/-0.305e-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) 0.1837741374025026107001296416309551e3+/-0.206e-27 y[1] (numeric) 0.1837741373346423907893609873706561e3+/-0.363e-27 absolute error 0.67860219910768654260299e-7+/-0.569e-27 relative error 0.3692588133995210536233385357819848e-7+/-0.309e-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) 0.2244621013563913855952306899753793e3+/-0.254e-27 y[1] (numeric) 0.2244621012729870958575513851452939e3+/-0.473e-27 absolute error 0.834042897376793048300854e-7+/-0.727e-27 relative error 0.3715740395981302786009769846715813e-7+/-0.323e-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 ) = sinh ( 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%