##############ECHO OF PROBLEM################# ##############temp/mult_div_sinh_cosh_tanhpostode.ode################# diff ( y , x , 1 ) = sinh(0.1) * cosh(0.05) / tanh(0.02); ! // BEGIN FIRST INPUT BLOCK Digits = 32; max_terms = 30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start = 0.1; x_end = 5.0 ; array_y_init[0 + 1] = exact_soln_y(x_start); glob_h = 0.05; glob_look_poles = true; glob_max_iter = 1000000; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_h = 0.005 ; glob_display_interval = 0.1; glob_look_poles = true; glob_max_iter = 10000; glob_max_minutes = 10; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return((sinh(0.1) * cosh(0.05) / tanh(0.02)) * x); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.5015267822632982 y[1] (numeric) = 0.5015267822632982 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.2000000000000001 y[1] (analytic) = 1.003053564526597 y[1] (numeric) = 1.003053564526596 absolute error = 1.110223024625157e-15 relative error = 1.106843207470321e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 1.504580346789895 y[1] (numeric) = 1.504580346789895 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 2.006107129053194 y[1] (numeric) = 2.006107129053195 absolute error = 8.881784197001252e-16 relative error = 4.427372829881281e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 2.507633911316493 y[1] (numeric) = 2.507633911316494 absolute error = 1.77635683940025e-15 relative error = 7.083796527810049e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 3.009160693579791 y[1] (numeric) = 3.009160693579794 absolute error = 2.664535259100376e-15 relative error = 8.854745659762561e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 3.51068747584309 y[1] (numeric) = 3.510687475843094 absolute error = 3.996802888650564e-15 relative error = 1.138467299112329e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 4.012214258106389 y[1] (numeric) = 4.012214258106393 absolute error = 4.440892098500626e-15 relative error = 1.10684320747032e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 4.513741040369687 y[1] (numeric) = 4.513741040369684 absolute error = 2.664535259100376e-15 relative error = 5.903163773175041e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 5.015267822632985 y[1] (numeric) = 5.015267822632975 absolute error = 1.06581410364015e-14 relative error = 2.125138958343015e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 5.541870944009437 y[1] (numeric) = 5.54187094400943 absolute error = 7.105427357601002e-15 relative error = 1.282135118155668e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 6.043397726272724 y[1] (numeric) = 6.043397726272721 absolute error = 3.552713678800501e-15 relative error = 5.878669317684711e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 6.544924508536012 y[1] (numeric) = 6.544924508536011 absolute error = 8.881784197001252e-16 relative error = 1.357049143258637e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 7.0464512907993 y[1] (numeric) = 7.046451290799302 absolute error = 2.664535259100376e-15 relative error = 3.781386046873716e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 7.547978073062587 y[1] (numeric) = 7.547978073062593 absolute error = 6.217248937900877e-15 relative error = 8.236972706755933e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 8.049504855325875 y[1] (numeric) = 8.049504855325884 absolute error = 8.881784197001252e-15 relative error = 1.103395097789736e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 8.551031637589162 y[1] (numeric) = 8.551031637589174 absolute error = 1.243449787580175e-14 relative error = 1.45415177990237e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 9.052558419852449 y[1] (numeric) = 9.052558419852465 absolute error = 1.598721155460225e-14 relative error = 1.766043455686733e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 9.554085202115736 y[1] (numeric) = 9.554085202115756 absolute error = 1.953992523340276e-14 relative error = 2.045190598580351e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 10.05561198437903 y[1] (numeric) = 10.05561198437905 absolute error = 2.131628207280301e-14 relative error = 2.11983935994318e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 10.55713876664231 y[1] (numeric) = 10.55713876664234 absolute error = 2.486899575160351e-14 relative error = 2.355656802597193e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 11.0586655489056 y[1] (numeric) = 11.05866554890563 absolute error = 2.664535259100376e-14 relative error = 2.409454601295964e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 11.56019233116889 y[1] (numeric) = 11.56019233116892 absolute error = 3.019806626980426e-14 relative error = 2.612246008086168e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 12.06171911343218 y[1] (numeric) = 12.06171911343221 absolute error = 3.375077994860476e-14 relative error = 2.798173264623548e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 12.56324589569546 y[1] (numeric) = 12.5632458956955 absolute error = 3.730349362740526e-14 relative error = 2.969256029621018e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 13.06477267795875 y[1] (numeric) = 13.06477267795879 absolute error = 4.085620730620576e-14 relative error = 3.127203841451696e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 13.56629946022204 y[1] (numeric) = 13.56629946022208 absolute error = 4.263256414560601e-14 relative error = 3.142534504019289e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 14.06782624248533 y[1] (numeric) = 14.06782624248537 absolute error = 4.618527782440651e-14 relative error = 3.28304295406531e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 14.56935302474861 y[1] (numeric) = 14.56935302474866 absolute error = 4.973799150320701e-14 relative error = 3.413877844727784e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 15.0708798070119 y[1] (numeric) = 15.07087980701195 absolute error = 5.329070518200751e-14 relative error = 3.536004922367797e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 15.57240658927519 y[1] (numeric) = 15.57240658927524 absolute error = 5.684341886080801e-14 relative error = 3.650265521576892e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 16.07393337153848 y[1] (numeric) = 16.07393337153854 absolute error = 6.394884621840902e-14 relative error = 3.978419266788855e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 16.57546015380176 y[1] (numeric) = 16.57546015380187 absolute error = 1.030286966852145e-13 relative error = 6.215736741497566e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 17.07698693606505 y[1] (numeric) = 17.07698693606519 absolute error = 1.4210854715202e-13 relative error = 8.321640561304151e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 17.57851371832834 y[1] (numeric) = 17.57851371832852 absolute error = 1.811883976188255e-13 relative error = 1.030737868525872e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 18.08004050059163 y[1] (numeric) = 18.08004050059185 absolute error = 2.202682480856311e-13 relative error = 1.218295103257226e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 18.58156728285491 y[1] (numeric) = 18.58156728285517 absolute error = 2.593480985524366e-13 relative error = 1.395727790904567e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 19.0830940651182 y[1] (numeric) = 19.0830940651185 absolute error = 2.984279490192421e-13 relative error = 1.563834187479773e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 19.58462084738149 y[1] (numeric) = 19.58462084738182 absolute error = 3.375077994860476e-13 relative error = 1.723330781413485e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 20.08614762964477 y[1] (numeric) = 20.08614762964515 absolute error = 3.765876499528531e-13 relative error = 1.874862501742516e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 20.58767441190806 y[1] (numeric) = 20.58767441190848 absolute error = 4.121147867408581e-13 relative error = 2.001754926250863e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 21.08920119417135 y[1] (numeric) = 21.0892011941718 absolute error = 4.511946372076636e-13 relative error = 2.139458166544331e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 21.59072797643464 y[1] (numeric) = 21.59072797643513 absolute error = 4.902744876744691e-13 relative error = 2.270764043757964e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 22.09225475869793 y[1] (numeric) = 22.09225475869846 absolute error = 5.293543381412746e-13 relative error = 2.396108246637265e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 22.59378154096121 y[1] (numeric) = 22.59378154096178 absolute error = 5.684341886080801e-13 relative error = 2.51588777902248e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 23.0953083232245 y[1] (numeric) = 23.09530832322511 absolute error = 6.075140390748857e-13 relative error = 2.630465160164038e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 23.59683510548779 y[1] (numeric) = 23.59683510548843 absolute error = 6.465938895416912e-13 relative error = 2.740172089397346e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 24.09836188775108 y[1] (numeric) = 24.09836188775176 absolute error = 6.856737400084967e-13 relative error = 2.845312653209913e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 24.59988867001436 y[1] (numeric) = 24.59988867001509 absolute error = 7.247535904753022e-13 relative error = 2.946166140006678e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 25.10141545227765 y[1] (numeric) = 25.10141545227841 absolute error = 7.638334409421077e-13 relative error = 3.042989517440934e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = sinh(0.1) * cosh(0.05) / tanh(0.02); Iterations = 981 Total Elapsed Time = 45 Seconds Elapsed Time(since restart) = 45 Seconds Time to Timeout = 9 Minutes 15 Seconds Percent Done = 100.2 %