##############ECHO OF PROBLEM################# ##############temp/sinh_sqrtpostode.ode################# diff ( y , x , 1 ) = sinh(sqrt(0.1 * x + 0.2)); ! /* 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(20.0 * sqrt(0.1 * x + 0.2) * cosh( sqrt(0.1 * x + 0.2)) - 20.0 * sinh( sqrt(0.1 * x + 0.2))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.6551348095261786 y[1] (numeric) = 0.6551348095261786 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) = 0.7031814518407211 y[1] (numeric) = 0.7031814518407207 absolute error = 4.440892098500626e-16 relative error = 6.315428381786357e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.7524136567096933 y[1] (numeric) = 0.7524136567096928 absolute error = 4.440892098500626e-16 relative error = 5.902194968018866e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.8028107639345183 y[1] (numeric) = 0.802810763934517 absolute error = 1.332267629550188e-15 relative error = 1.659503944641748e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.8543535421888593 y[1] (numeric) = 0.8543535421888612 absolute error = 1.887379141862766e-15 relative error = 2.209131288936063e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 0.9070240425590019 y[1] (numeric) = 0.9070240425590025 absolute error = 5.551115123125783e-16 relative error = 6.120141101733455e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 0.9608054721466561 y[1] (numeric) = 0.9608054721466568 absolute error = 6.661338147750939e-16 relative error = 6.933076820293297e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 1.015682084341464 y[1] (numeric) = 1.015682084341468 absolute error = 3.552713678800501e-15 relative error = 3.49785994414184e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 1.071639083045625 y[1] (numeric) = 1.071639083045626 absolute error = 1.110223024625157e-15 relative error = 1.036004604712507e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 1.128662538655146 y[1] (numeric) = 1.128662538655146 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 1.189670576872135 y[1] (numeric) = 1.189670576872138 absolute error = 3.552713678800501e-15 relative error = 2.986300365720775e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 1.248839993637084 y[1] (numeric) = 1.248839993637088 absolute error = 3.108624468950438e-15 relative error = 2.489209574316221e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 1.30903800777019 y[1] (numeric) = 1.309038007770193 absolute error = 2.664535259100376e-15 relative error = 2.035491134164343e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 1.370253523877909 y[1] (numeric) = 1.370253523877918 absolute error = 8.215650382226158e-15 relative error = 5.995715565813921e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 1.43247601449842 y[1] (numeric) = 1.432476014498426 absolute error = 6.661338147750939e-15 relative error = 4.650226656732819e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 1.495695478519103 y[1] (numeric) = 1.495695478519113 absolute error = 9.769962616701378e-15 relative error = 6.532053320355475e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 1.559902403699402 y[1] (numeric) = 1.559902403699413 absolute error = 1.088018564132653e-14 relative error = 6.974914337924936e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 1.625087732793886 y[1] (numeric) = 1.625087732793897 absolute error = 1.154631945610163e-14 relative error = 7.105043760468825e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 1.691242832844398 y[1] (numeric) = 1.691242832844413 absolute error = 1.48769885299771e-14 relative error = 8.796482823792016e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 1.758359467271442 y[1] (numeric) = 1.75835946727146 absolute error = 1.84297022087776e-14 relative error = 1.048119144680703e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 1.826429770446291 y[1] (numeric) = 1.826429770446305 absolute error = 1.443289932012704e-14 relative error = 7.902247079886534e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 1.895446224468434 y[1] (numeric) = 1.895446224468452 absolute error = 1.820765760385257e-14 relative error = 9.606000618117661e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 1.965401637909481 y[1] (numeric) = 1.965401637909501 absolute error = 2.020605904817785e-14 relative error = 1.028088033429657e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 2.036289126315246 y[1] (numeric) = 2.036289126315269 absolute error = 2.309263891220326e-14 relative error = 1.134055012806084e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 2.108102094284269 y[1] (numeric) = 2.108102094284293 absolute error = 2.398081733190338e-14 relative error = 1.137554836500706e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 2.180834218963266 y[1] (numeric) = 2.18083421896329 absolute error = 2.398081733190338e-14 relative error = 1.099616702791076e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 2.254479434819321 y[1] (numeric) = 2.254479434819348 absolute error = 2.664535259100376e-14 relative error = 1.181884925605417e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 2.329031919565207 y[1] (numeric) = 2.329031919565234 absolute error = 2.708944180085382e-14 relative error = 1.163120246368757e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 2.404486081128406 y[1] (numeric) = 2.404486081128435 absolute error = 2.886579864025407e-14 relative error = 1.200497639258847e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 2.48083654556696 y[1] (numeric) = 2.480836545566991 absolute error = 3.108624468950438e-14 relative error = 1.253054932016896e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 2.558078145845875 y[1] (numeric) = 2.558078145845912 absolute error = 3.641531520770513e-14 relative error = 1.423541937795796e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 2.636205911397315 y[1] (numeric) = 2.636205911397354 absolute error = 3.907985046680551e-14 relative error = 1.482427844420216e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 2.715215058395889 y[1] (numeric) = 2.715215058395932 absolute error = 4.352074256530614e-14 relative error = 1.602846980047967e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 2.795100980687707 y[1] (numeric) = 2.795100980687744 absolute error = 3.68594044175552e-14 relative error = 1.318714589284223e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 2.875859241317924 y[1] (numeric) = 2.875859241317968 absolute error = 4.307665335545607e-14 relative error = 1.497870714135344e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 2.957485564607431 y[1] (numeric) = 2.957485564607474 absolute error = 4.263256414560601e-14 relative error = 1.441513854058826e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 3.039975828733783 y[1] (numeric) = 3.039975828733826 absolute error = 4.263256414560601e-14 relative error = 1.402398129045763e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 3.123326058776286 y[1] (numeric) = 3.123326058776336 absolute error = 5.018208071305708e-14 relative error = 1.606687222810107e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 3.207532420188702 y[1] (numeric) = 3.207532420188754 absolute error = 5.195843755245733e-14 relative error = 1.619888149077557e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 3.292591212666521 y[1] (numeric) = 3.292591212666573 absolute error = 5.151434834260726e-14 relative error = 1.564553417516052e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 3.37849886437892 y[1] (numeric) = 3.378498864378976 absolute error = 5.595524044110789e-14 relative error = 1.656216050005815e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 3.465251926538151 y[1] (numeric) = 3.465251926538204 absolute error = 5.329070518200751e-14 relative error = 1.537859477802698e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 3.552847068281479 y[1] (numeric) = 3.552847068281537 absolute error = 5.861977570020827e-14 relative error = 1.649938051754161e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 3.641281071843232 y[1] (numeric) = 3.641281071843289 absolute error = 5.773159728050814e-14 relative error = 1.585474895825171e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 3.730550827996093 y[1] (numeric) = 3.730550827996153 absolute error = 5.995204332975845e-14 relative error = 1.607056064746405e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 3.820653331742957 y[1] (numeric) = 3.820653331743018 absolute error = 6.084022174945858e-14 relative error = 1.592403614428522e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 3.911585678241899 y[1] (numeric) = 3.911585678241962 absolute error = 6.306066779870889e-14 relative error = 1.612151004373555e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 4.003345058948479 y[1] (numeric) = 4.003345058948544 absolute error = 6.483702463810914e-14 relative error = 1.619571225647466e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 4.095928757960772 y[1] (numeric) = 4.095928757960841 absolute error = 6.838973831690964e-14 relative error = 1.669700386853375e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 4.189334148553751 y[1] (numeric) = 4.189334148553822 absolute error = 7.105427357601002e-14 relative error = 1.696075582811638e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = sinh(sqrt(0.1 * x + 0.2)); Iterations = 981 Total Elapsed Time = 1 Minutes 51 Seconds Elapsed Time(since restart) = 1 Minutes 50 Seconds Time to Timeout = 8 Minutes 9 Seconds Percent Done = 100.2 %