##############ECHO OF PROBLEM################# ##############temp/lin_tanhpostode.ode################# diff ( y , x , 1 ) = tanh ( 3.0 * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(1.1); x_end=c(2.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; 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=true; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(ln(cosh(c(3.0)*c(x) + c(1.0)))/c(3.0)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 1.20234563609611 y[1] (numeric) = 1.20234563609611 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 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] = 1.109999999999999 y[1] (closed_form) = 1.212342062905878 y[1] (numeric) = 1.212342062905879 absolute error = 1.77635683940025e-15 relative error = 1.465227425288271e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 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] = 1.119999999999998 y[1] (closed_form) = 1.222338697767023 y[1] (numeric) = 1.222338697767025 absolute error = 2.442490654175344e-15 relative error = 1.998211018465916e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 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] = 1.129999999999997 y[1] (closed_form) = 1.232335528567535 y[1] (numeric) = 1.232335528567539 absolute error = 3.774758283725532e-15 relative error = 3.063092961470733e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 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] = 1.139999999999996 y[1] (closed_form) = 1.242332543900308 y[1] (numeric) = 1.242332543900313 absolute error = 4.884981308350689e-15 relative error = 3.932104437201872e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 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] = 1.149999999999995 y[1] (closed_form) = 1.252329733022132 y[1] (numeric) = 1.252329733022138 absolute error = 6.439293542825908e-15 relative error = 5.141851521233593e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 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] = 1.159999999999993 y[1] (closed_form) = 1.262327085815085 y[1] (numeric) = 1.262327085815093 absolute error = 7.105427357601002e-15 relative error = 5.628832207947929e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 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] = 1.169999999999992 y[1] (closed_form) = 1.272324592750153 y[1] (numeric) = 1.272324592750161 absolute error = 8.659739592076221e-15 relative error = 6.806234542207532e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 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] = 1.179999999999991 y[1] (closed_form) = 1.282322244852971 y[1] (numeric) = 1.28232224485298 absolute error = 9.325873406851315e-15 relative error = 7.272644176831391e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 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] = 1.18999999999999 y[1] (closed_form) = 1.292320033671554 y[1] (numeric) = 1.292320033671565 absolute error = 1.110223024625157e-14 relative error = 8.590929457859988e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 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] = 1.199999999999989 y[1] (closed_form) = 1.302317951245908 y[1] (numeric) = 1.30231795124592 absolute error = 1.199040866595169e-14 relative error = 9.20697488234778e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 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] = 1.209999999999988 y[1] (closed_form) = 1.312315990079394 y[1] (numeric) = 1.312315990079407 absolute error = 1.265654248072678e-14 relative error = 9.644432115744527e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 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] = 1.219999999999987 y[1] (closed_form) = 1.322314143111777 y[1] (numeric) = 1.322314143111791 absolute error = 1.354472090042691e-14 relative error = 1.024319445646431e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 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] = 1.229999999999986 y[1] (closed_form) = 1.332312403693823 y[1] (numeric) = 1.332312403693839 absolute error = 1.509903313490213e-14 relative error = 1.133295246147991e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 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] = 1.239999999999985 y[1] (closed_form) = 1.342310765563386 y[1] (numeric) = 1.342310765563402 absolute error = 1.598721155460225e-14 relative error = 1.191021629621826e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 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] = 1.249999999999984 y[1] (closed_form) = 1.352309222822878 y[1] (numeric) = 1.352309222822895 absolute error = 1.709743457922741e-14 relative error = 1.264313981645216e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.259999999999982 y[1] (closed_form) = 1.362307769918055 y[1] (numeric) = 1.362307769918073 absolute error = 1.77635683940025e-14 relative error = 1.303932105963913e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.269999999999981 y[1] (closed_form) = 1.37230640161803 y[1] (numeric) = 1.37230640161805 absolute error = 1.909583602355269e-14 relative error = 1.391514023474464e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.27999999999998 y[1] (closed_form) = 1.382305112996461 y[1] (numeric) = 1.382305112996481 absolute error = 1.998401444325282e-14 relative error = 1.445702128666291e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.289999999999979 y[1] (closed_form) = 1.392303899413814 y[1] (numeric) = 1.392303899413835 absolute error = 2.109423746787797e-14 relative error = 1.515059857029707e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.299999999999978 y[1] (closed_form) = 1.40230275650068 y[1] (numeric) = 1.402302756500702 absolute error = 2.264854970235319e-14 relative error = 1.61509699651954e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.309999999999977 y[1] (closed_form) = 1.41230168014204 y[1] (numeric) = 1.412301680142064 absolute error = 2.375877272697835e-14 relative error = 1.682273204163351e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.319999999999976 y[1] (closed_form) = 1.422300666462472 y[1] (numeric) = 1.422300666462496 absolute error = 2.464695114667848e-14 relative error = 1.732893172860564e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.329999999999975 y[1] (closed_form) = 1.432299711812186 y[1] (numeric) = 1.432299711812212 absolute error = 2.642330798607873e-14 relative error = 1.844816958920366e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.339999999999974 y[1] (closed_form) = 1.442298812753905 y[1] (numeric) = 1.442298812753932 absolute error = 2.708944180085382e-14 relative error = 1.878212861392406e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.349999999999973 y[1] (closed_form) = 1.452297966050485 y[1] (numeric) = 1.452297966050514 absolute error = 2.864375403532904e-14 relative error = 1.972305594644985e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.359999999999971 y[1] (closed_form) = 1.462297168653268 y[1] (numeric) = 1.462297168653298 absolute error = 2.97539770599542e-14 relative error = 2.034742164436845e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.36999999999997 y[1] (closed_form) = 1.472296417691104 y[1] (numeric) = 1.472296417691136 absolute error = 3.153033389935445e-14 relative error = 2.141575128519377e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.379999999999969 y[1] (closed_form) = 1.482295710460027 y[1] (numeric) = 1.482295710460058 absolute error = 3.197442310920451e-14 relative error = 2.157088014461118e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.389999999999968 y[1] (closed_form) = 1.492295044413508 y[1] (numeric) = 1.492295044413541 absolute error = 3.33066907387547e-14 relative error = 2.231910563761517e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.399999999999967 y[1] (closed_form) = 1.502294417153302 y[1] (numeric) = 1.502294417153336 absolute error = 3.419486915845482e-14 relative error = 2.2761762786319e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.409999999999966 y[1] (closed_form) = 1.512293826420807 y[1] (numeric) = 1.512293826420843 absolute error = 3.552713678800501e-14 relative error = 2.349221835553491e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.419999999999965 y[1] (closed_form) = 1.522293270088938 y[1] (numeric) = 1.522293270088974 absolute error = 3.61932706027801e-14 relative error = 2.37754914338323e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.429999999999964 y[1] (closed_form) = 1.532292746154465 y[1] (numeric) = 1.532292746154503 absolute error = 3.752553823233029e-14 relative error = 2.448979695721112e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.439999999999963 y[1] (closed_form) = 1.542292252730808 y[1] (numeric) = 1.542292252730847 absolute error = 3.841371665203042e-14 relative error = 2.49068985362628e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.449999999999962 y[1] (closed_form) = 1.55229178804124 y[1] (numeric) = 1.552291788041279 absolute error = 3.97459842815806e-14 relative error = 2.560471207010255e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.45999999999996 y[1] (closed_form) = 1.562291350412493 y[1] (numeric) = 1.562291350412534 absolute error = 4.063416270128073e-14 relative error = 2.600933730481965e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.469999999999959 y[1] (closed_form) = 1.572290938268734 y[1] (numeric) = 1.572290938268776 absolute error = 4.174438572590589e-14 relative error = 2.655003899715345e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.479999999999958 y[1] (closed_form) = 1.582290550125895 y[1] (numeric) = 1.582290550125937 absolute error = 4.241051954068098e-14 relative error = 2.680324390315457e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.489999999999957 y[1] (closed_form) = 1.59229018458632 y[1] (numeric) = 1.592290184586364 absolute error = 4.39648317751562e-14 relative error = 2.761106750562451e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.499999999999956 y[1] (closed_form) = 1.602289840333747 y[1] (numeric) = 1.602289840333792 absolute error = 4.440892098500626e-14 relative error = 2.771590998527217e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.509999999999955 y[1] (closed_form) = 1.612289516128558 y[1] (numeric) = 1.612289516128604 absolute error = 4.574118861455645e-14 relative error = 2.837033185230314e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.519999999999954 y[1] (closed_form) = 1.622289210803321 y[1] (numeric) = 1.622289210803368 absolute error = 4.707345624410664e-14 relative error = 2.901668576147216e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.529999999999953 y[1] (closed_form) = 1.632288923258585 y[1] (numeric) = 1.632288923258634 absolute error = 4.840572387365683e-14 relative error = 2.965511998759576e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.539999999999952 y[1] (closed_form) = 1.642288652458925 y[1] (numeric) = 1.642288652458975 absolute error = 4.951594689828198e-14 relative error = 3.015057482382526e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.549999999999951 y[1] (closed_form) = 1.652288397429208 y[1] (numeric) = 1.652288397429259 absolute error = 5.062616992290714e-14 relative error = 3.064003233435294e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.559999999999949 y[1] (closed_form) = 1.662288157251087 y[1] (numeric) = 1.662288157251139 absolute error = 5.129230373768223e-14 relative error = 3.0856445384598e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.569999999999948 y[1] (closed_form) = 1.672287931059692 y[1] (numeric) = 1.672287931059745 absolute error = 5.306866057708248e-14 relative error = 3.173416466831404e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.579999999999947 y[1] (closed_form) = 1.682287718040519 y[1] (numeric) = 1.682287718040573 absolute error = 5.395683899678261e-14 relative error = 3.207349041317974e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.589999999999946 y[1] (closed_form) = 1.692287517426492 y[1] (numeric) = 1.692287517426547 absolute error = 5.52891066263328e-14 relative error = 3.267122522443022e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.599999999999945 y[1] (closed_form) = 1.702287328495206 y[1] (numeric) = 1.702287328495263 absolute error = 5.662137425588298e-14 relative error = 3.326193722298065e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.609999999999944 y[1] (closed_form) = 1.712287150566323 y[1] (numeric) = 1.712287150566381 absolute error = 5.81756864903582e-14 relative error = 3.397542665149191e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.619999999999943 y[1] (closed_form) = 1.722286982999125 y[1] (numeric) = 1.722286982999184 absolute error = 5.906386491005833e-14 relative error = 3.429385781410642e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.629999999999942 y[1] (closed_form) = 1.732286825190204 y[1] (numeric) = 1.732286825190264 absolute error = 6.017408793468348e-14 relative error = 3.473679246395954e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.639999999999941 y[1] (closed_form) = 1.742286676571291 y[1] (numeric) = 1.742286676571352 absolute error = 6.106226635438361e-14 relative error = 3.504719813076356e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.64999999999994 y[1] (closed_form) = 1.752286536607208 y[1] (numeric) = 1.752286536607271 absolute error = 6.23945339839338e-14 relative error = 3.560749493900844e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.659999999999938 y[1] (closed_form) = 1.762286404793946 y[1] (numeric) = 1.762286404794009 absolute error = 6.261657858885883e-14 relative error = 3.553144279983265e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.669999999999937 y[1] (closed_form) = 1.772286280656843 y[1] (numeric) = 1.772286280656907 absolute error = 6.417089082333405e-14 relative error = 3.620797132140024e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.679999999999936 y[1] (closed_form) = 1.782286163748879 y[1] (numeric) = 1.782286163748944 absolute error = 6.505906924303417e-14 relative error = 3.650315564712024e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.689999999999935 y[1] (closed_form) = 1.792286053649068 y[1] (numeric) = 1.792286053649134 absolute error = 6.616929226765933e-14 relative error = 3.691893497298583e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.699999999999934 y[1] (closed_form) = 1.802285949960937 y[1] (numeric) = 1.802285949961005 absolute error = 6.750155989720952e-14 relative error = 3.745330195725742e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.709999999999933 y[1] (closed_form) = 1.812285852311103 y[1] (numeric) = 1.812285852311172 absolute error = 6.861178292183467e-14 relative error = 3.785924987183343e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.719999999999932 y[1] (closed_form) = 1.822285760347927 y[1] (numeric) = 1.822285760347997 absolute error = 6.972200594645983e-14 relative error = 3.826074233996532e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.729999999999931 y[1] (closed_form) = 1.832285673740246 y[1] (numeric) = 1.832285673740317 absolute error = 7.105427357601002e-14 relative error = 3.877903680323325e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.73999999999993 y[1] (closed_form) = 1.842285592176183 y[1] (numeric) = 1.842285592176255 absolute error = 7.172040739078511e-14 relative error = 3.8930124458101e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.749999999999929 y[1] (closed_form) = 1.852285515362023 y[1] (numeric) = 1.852285515362096 absolute error = 7.30526750203353e-14 relative error = 3.943920870431113e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.759999999999927 y[1] (closed_form) = 1.862285443021155 y[1] (numeric) = 1.862285443021229 absolute error = 7.394085344003543e-14 relative error = 3.970436095987648e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.769999999999926 y[1] (closed_form) = 1.872285374893077 y[1] (numeric) = 1.872285374893152 absolute error = 7.549516567451064e-14 relative error = 4.032246723009417e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.779999999999925 y[1] (closed_form) = 1.882285310732456 y[1] (numeric) = 1.882285310732533 absolute error = 7.66053886991358e-14 relative error = 4.069807497425894e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.789999999999924 y[1] (closed_form) = 1.892285250308248 y[1] (numeric) = 1.892285250308326 absolute error = 7.793765632868599e-14 relative error = 4.118705481427294e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.799999999999923 y[1] (closed_form) = 1.902285193402862 y[1] (numeric) = 1.902285193402941 absolute error = 7.882583474838611e-14 relative error = 4.143744325075686e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.809999999999922 y[1] (closed_form) = 1.912285139811378 y[1] (numeric) = 1.912285139811458 absolute error = 8.038014698286133e-14 relative error = 4.203355729197884e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.819999999999921 y[1] (closed_form) = 1.922285089340812 y[1] (numeric) = 1.922285089340893 absolute error = 8.171241461241152e-14 relative error = 4.250795840092183e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.82999999999992 y[1] (closed_form) = 1.932285041809415 y[1] (numeric) = 1.932285041809498 absolute error = 8.282263763703668e-14 relative error = 4.286253624334874e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.839999999999919 y[1] (closed_form) = 1.942284997046025 y[1] (numeric) = 1.942284997046109 absolute error = 8.37108160567368e-14 relative error = 4.309914156987804e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.849999999999917 y[1] (closed_form) = 1.952284954889447 y[1] (numeric) = 1.952284954889532 absolute error = 8.526512829121202e-14 relative error = 4.367453023579767e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.859999999999916 y[1] (closed_form) = 1.962284915187871 y[1] (numeric) = 1.962284915187957 absolute error = 8.593126210598712e-14 relative error = 4.379142979742061e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.869999999999915 y[1] (closed_form) = 1.972284877798331 y[1] (numeric) = 1.972284877798419 absolute error = 8.72635297355373e-14 relative error = 4.424489115028347e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.879999999999914 y[1] (closed_form) = 1.982284842586185 y[1] (numeric) = 1.982284842586273 absolute error = 8.837375276016246e-14 relative error = 4.458176285344834e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.889999999999913 y[1] (closed_form) = 1.99228480942463 y[1] (numeric) = 1.99228480942472 absolute error = 8.992806499463768e-14 relative error = 4.513815723998257e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.899999999999912 y[1] (closed_form) = 2.002284778194252 y[1] (numeric) = 2.002284778194342 absolute error = 9.015010959956271e-14 relative error = 4.502362030682969e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.909999999999911 y[1] (closed_form) = 2.012284748782586 y[1] (numeric) = 2.012284748782677 absolute error = 9.14823772291129e-14 relative error = 4.546194433191372e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.91999999999991 y[1] (closed_form) = 2.02228472108372 y[1] (numeric) = 2.022284721083812 absolute error = 9.192646643896296e-14 relative error = 4.545673785721953e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.929999999999909 y[1] (closed_form) = 2.032284694997907 y[1] (numeric) = 2.032284694998001 absolute error = 9.325873406851315e-14 relative error = 4.588861703188154e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.939999999999908 y[1] (closed_form) = 2.042284670431213 y[1] (numeric) = 2.042284670431308 absolute error = 9.459100169806334e-14 relative error = 4.631626681019505e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.949999999999906 y[1] (closed_form) = 2.05228464729517 y[1] (numeric) = 2.052284647295266 absolute error = 9.636735853746359e-14 relative error = 4.69561367447113e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.959999999999905 y[1] (closed_form) = 2.062284625506464 y[1] (numeric) = 2.06228462550656 absolute error = 9.681144774731365e-14 relative error = 4.694378581401601e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.969999999999904 y[1] (closed_form) = 2.072284604986631 y[1] (numeric) = 2.072284604986729 absolute error = 9.769962616701378e-14 relative error = 4.714585338901558e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.979999999999903 y[1] (closed_form) = 2.08228458566178 y[1] (numeric) = 2.082284585661878 absolute error = 9.85878045867139e-14 relative error = 4.734598011509618e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.989999999999902 y[1] (closed_form) = 2.092284567462318 y[1] (numeric) = 2.092284567462418 absolute error = 9.992007221626409e-14 relative error = 4.775644468737575e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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] = 1.999999999999901 y[1] (closed_form) = 2.102284550322711 y[1] (numeric) = 2.102284550322811 absolute error = 1.003641614261142e-13 relative error = 4.774052181028861e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 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 ) = tanh ( 3.0 * x + 1.0 ) ; Iterations = 901 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.2 %