##############ECHO OF PROBLEM################# ##############temp/cosh_sqrtpostode.ode################# diff ( y , x , 1 ) = cosh(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) * sinh( sqrt(0.1 * x + 0.2)) - 20.0 * cosh( 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) = -17.78845697688962 y[1] (numeric) = -17.78845697688962 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) = -17.67751295160642 y[1] (numeric) = -17.67751295160642 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = -17.5660503901931 y[1] (numeric) = -17.5660503901931 absolute error = 3.552713678800501e-15 relative error = 2.022488607219261e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 0.4000000000000002 y[1] (analytic) = -17.45406844041495 y[1] (numeric) = -17.45406844041494 absolute error = 1.06581410364015e-14 relative error = 6.106393516667177e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = -17.34156624919014 y[1] (numeric) = -17.34156624919013 absolute error = 7.105427357601002e-15 relative error = 4.097338876719298e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = -17.22854296258915 y[1] (numeric) = -17.22854296258915 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 0.7000000000000005 y[1] (analytic) = -17.11499772583412 y[1] (numeric) = -17.11499772583411 absolute error = 3.552713678800501e-15 relative error = 2.075789746345033e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = -17.00092968329827 y[1] (numeric) = -17.00092968329826 absolute error = 3.552713678800501e-15 relative error = 2.089717294866934e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = -16.88633797850531 y[1] (numeric) = -16.88633797850531 absolute error = 3.552713678800501e-15 relative error = 2.103898242071647e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = -16.77122175412881 y[1] (numeric) = -16.77122175412881 absolute error = 3.552713678800501e-15 relative error = 2.118339218742891e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = -16.64978426531333 y[1] (numeric) = -16.64978426531333 absolute error = 3.552713678800501e-15 relative error = 2.133789616843208e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = -16.53359009198267 y[1] (numeric) = -16.53359009198267 absolute error = 3.552713678800501e-15 relative error = 2.148785387224068e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = -16.41686877896596 y[1] (numeric) = -16.41686877896595 absolute error = 3.552713678800501e-15 relative error = 2.164062907874613e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used x[1] = 1.404999999999992 y[1] (analytic) = -16.29961946548753 y[1] (numeric) = -16.29961946548753 absolute error = 3.552713678800501e-15 relative error = 2.179629828980328e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = -16.18184128991858 y[1] (numeric) = -16.18184128991856 absolute error = 1.4210854715202e-14 relative error = 8.78197632803103e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = -16.06353338977645 y[1] (numeric) = -16.06353338977643 absolute error = 1.77635683940025e-14 relative error = 1.105831946370406e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = -15.94469490172414 y[1] (numeric) = -15.94469490172411 absolute error = 2.842170943040401e-14 relative error = 1.782518236039167e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = -15.8253249615696 y[1] (numeric) = -15.82532496156956 absolute error = 3.552713678800501e-14 relative error = 2.244954645435687e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = -15.70542270426518 y[1] (numeric) = -15.70542270426515 absolute error = 3.552713678800501e-14 relative error = 2.262093638419345e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = -15.58498726390702 y[1] (numeric) = -15.58498726390698 absolute error = 3.730349362740526e-14 relative error = 2.39355303894253e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = -15.4640177737344 y[1] (numeric) = -15.46401777373435 absolute error = 4.618527782440651e-14 relative error = 2.986628604556579e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = -15.34251336612918 y[1] (numeric) = -15.34251336612913 absolute error = 4.796163466380676e-14 relative error = 3.126061129572747e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = -15.22047317261518 y[1] (numeric) = -15.22047317261512 absolute error = 5.506706202140776e-14 relative error = 3.617959927848035e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = -15.09789632385753 y[1] (numeric) = -15.09789632385748 absolute error = 5.684341886080801e-14 relative error = 3.764989349607909e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = -14.97478194966214 y[1] (numeric) = -14.97478194966207 absolute error = 6.394884621840902e-14 relative error = 4.270435885702619e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = -14.851129178975 y[1] (numeric) = -14.85112917897492 absolute error = 7.105427357601002e-14 relative error = 4.784435763753425e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = -14.72693713988162 y[1] (numeric) = -14.72693713988155 absolute error = 7.105427357601002e-14 relative error = 4.824782838489196e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = -14.60220495960645 y[1] (numeric) = -14.60220495960638 absolute error = 6.927791673660977e-14 relative error = 4.744346277034926e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = -14.47693176451218 y[1] (numeric) = -14.47693176451211 absolute error = 7.460698725481052e-14 relative error = 5.153508248045851e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = -14.35111668009923 y[1] (numeric) = -14.35111668009915 absolute error = 7.638334409421077e-14 relative error = 5.322466940857081e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = -14.22475883100504 y[1] (numeric) = -14.22475883100497 absolute error = 7.460698725481052e-14 relative error = 5.244868341260953e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = -14.09785734100356 y[1] (numeric) = -14.09785734100348 absolute error = 7.283063041541027e-14 relative error = 5.166077982899054e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = -13.97041133300454 y[1] (numeric) = -13.97041133300447 absolute error = 7.638334409421077e-14 relative error = 5.467508598960015e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = -13.84241992905299 y[1] (numeric) = -13.84241992905291 absolute error = 7.993605777301127e-14 relative error = 5.774717006326218e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = -13.71388225032852 y[1] (numeric) = -13.71388225032845 absolute error = 7.638334409421077e-14 relative error = 5.56978269901515e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = -13.58479741714478 y[1] (numeric) = -13.5847974171447 absolute error = 8.348877145181177e-14 relative error = 6.145750200620897e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = -13.45516454894878 y[1] (numeric) = -13.45516454894868 absolute error = 9.414691248821327e-14 relative error = 6.997083695685369e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = -13.32498276432031 y[1] (numeric) = -13.32498276432021 absolute error = 1.012523398458143e-13 relative error = 7.598684488878513e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = -13.19425118097136 y[1] (numeric) = -13.19425118097125 absolute error = 1.048050535246148e-13 relative error = 7.943236193332729e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = -13.06296891574543 y[1] (numeric) = -13.06296891574532 absolute error = 1.101341240428155e-13 relative error = 8.431017845419929e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = -12.93113508461698 y[1] (numeric) = -12.93113508461687 absolute error = 1.13686837721616e-13 relative error = 8.791713718686544e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = -12.7987488026908 y[1] (numeric) = -12.79874880269068 absolute error = 1.190159082398168e-13 relative error = 9.299026809151454e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = -12.66580918420134 y[1] (numeric) = -12.66580918420122 absolute error = 1.20792265079217e-13 relative error = 9.536877061900385e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 4.404999999999928 y[1] (analytic) = -12.5323153425122 y[1] (numeric) = -12.53231534251208 absolute error = 1.225686219186173e-13 relative error = 9.780205697732422e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 4.504999999999926 y[1] (analytic) = -12.39826639011541 y[1] (numeric) = -12.39826639011528 absolute error = 1.261213355974178e-13 relative error = 1.017249764031274e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = -12.26366143863086 y[1] (numeric) = -12.26366143863073 absolute error = 1.27897692436818e-13 relative error = 1.042899733304255e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = -12.12849959880571 y[1] (numeric) = -12.12849959880558 absolute error = 1.27897692436818e-13 relative error = 1.054521966174712e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = -11.99277998051371 y[1] (numeric) = -11.99277998051358 absolute error = 1.314504061156185e-13 relative error = 1.096079527258932e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 4.904999999999918 y[1] (analytic) = -11.85650169275463 y[1] (numeric) = -11.8565016927545 absolute error = 1.314504061156185e-13 relative error = 1.108677833664431e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = -11.71966384365362 y[1] (numeric) = -11.71966384365348 absolute error = 1.385558334732195e-13 relative error = 1.182250918811546e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2)); Iterations = 981 Total Elapsed Time = 1 Minutes 55 Seconds Elapsed Time(since restart) = 1 Minutes 54 Seconds Time to Timeout = 8 Minutes 5 Seconds Percent Done = 100.2 %