##############ECHO OF PROBLEM################# ##############temp/diffpostode.ode################# diff ( y , x , 2 ) = diff ( y , x , 1 ) ; ! // BEGIN FIRST INPUT BLOCK Digits = 32; max_terms = 30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start = -4.0; x_end = 1.0 ; array_y_init[0 + 1] = exact_soln_y(x_start); array_y_init[1 + 1] = exact_soln_yp(x_start); glob_h = 0.00001 ; glob_look_poles = true; glob_max_iter = 10; // 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(1.0 + exp(x)); } double exact_soln_yp (double x) { return(exp(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = -4 y[1] (analytic) = 1.018315638888734 y[1] (numeric) = 1.018315638888734 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -3.895000000000002 y[1] (analytic) = 1.020343374449161 y[1] (numeric) = 1.020238780972052 absolute error = 0.000104593477108228 relative error = 0.01025081161179622 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -3.795000000000004 y[1] (analytic) = 1.022482905816736 y[1] (numeric) = 1.022070344860927 absolute error = 0.0004125609558087717 relative error = 0.04034893429139802 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -3.695000000000007 y[1] (analytic) = 1.02484745366249 y[1] (numeric) = 1.023901908749801 absolute error = 0.0009455449126887228 relative error = 0.09226201512328842 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -3.595000000000009 y[1] (analytic) = 1.027460683176016 y[1] (numeric) = 1.025733472638676 absolute error = 0.001727210537340262 relative error = 0.1681047815865059 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -3.495000000000011 y[1] (analytic) = 1.030348748436622 y[1] (numeric) = 1.02756503652755 absolute error = 0.002783711909071895 relative error = 0.2701718144750214 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -3.395000000000013 y[1] (analytic) = 1.033540554172148 y[1] (numeric) = 1.029396600416424 absolute error = 0.004143953755723961 relative error = 0.4009473783100085 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -3.295000000000015 y[1] (analytic) = 1.037068045047199 y[1] (numeric) = 1.031228164305299 absolute error = 0.005839880741900227 relative error = 0.563114519803225 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -3.195000000000017 y[1] (analytic) = 1.040966525376082 y[1] (numeric) = 1.033059728194173 absolute error = 0.00790679718190912 relative error = 0.7595630588651771 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -3.095000000000019 y[1] (analytic) = 1.045275012460254 y[1] (numeric) = 1.034891292083048 absolute error = 0.01038372037720658 relative error = 0.9933960205139237 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -2.995000000000021 y[1] (analytic) = 1.050036627086585 y[1] (numeric) = 1.036722855971922 absolute error = 0.01331377111466336 relative error = 1.267933972132338 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -2.895000000000024 y[1] (analytic) = 1.05529902509469 y[1] (numeric) = 1.038554419860796 absolute error = 0.01674460523389376 relative error = 1.586716640090831 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -2.795000000000026 y[1] (analytic) = 1.061114874332587 y[1] (numeric) = 1.040385983749671 absolute error = 0.02072889058291616 relative error = 1.953501084974808 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -2.695000000000028 y[1] (analytic) = 1.067542381774223 y[1] (numeric) = 1.042217547638545 absolute error = 0.02532483413567754 relative error = 2.372255618890601 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -2.59500000000003 y[1] (analytic) = 1.074645876074433 y[1] (numeric) = 1.04404911152742 absolute error = 0.03059676454701377 relative error = 2.847148556395199 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -2.495000000000032 y[1] (analytic) = 1.082496451391742 y[1] (numeric) = 1.045880675416294 absolute error = 0.03661577597544841 relative error = 3.382530809073073 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -2.395000000000034 y[1] (analytic) = 1.091172678922595 y[1] (numeric) = 1.047712239305168 absolute error = 0.04346043961742652 relative error = 3.982911271233313 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -2.295000000000036 y[1] (analytic) = 1.1007613932683 y[1] (numeric) = 1.049543803194043 absolute error = 0.0512175900742573 relative error = 4.652923911347017 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -2.195000000000038 y[1] (analytic) = 1.111358561504908 y[1] (numeric) = 1.051375367082917 absolute error = 0.05998319442199129 relative error = 5.397285493600471 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -2.095000000000041 y[1] (analytic) = 1.123070243653963 y[1] (numeric) = 1.053206930971792 absolute error = 0.06986331268217127 relative error = 6.220742921196776 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -1.995000000000043 y[1] (analytic) = 1.136013654166843 y[1] (numeric) = 1.055038494860666 absolute error = 0.08097515930617738 relative error = 7.128009334145273 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -1.895000000000045 y[1] (analytic) = 1.150318335046394 y[1] (numeric) = 1.05687005874954 absolute error = 0.09344827629685337 relative error = 8.12368832607406 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -1.795000000000047 y[1] (analytic) = 1.166127452346825 y[1] (numeric) = 1.058701622638415 absolute error = 0.1074258297084105 relative error = 9.212185982948657 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -1.695000000000049 y[1] (analytic) = 1.183599229027709 y[1] (numeric) = 1.060533186527289 absolute error = 0.1230660425004197 relative error = 10.39761090428513 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -1.595000000000051 y[1] (analytic) = 1.202908528502534 y[1] (numeric) = 1.062364750416164 absolute error = 0.1405437780863701 relative error = 11.68366295160689 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -1.495000000000053 y[1] (analytic) = 1.224248604730523 y[1] (numeric) = 1.064196314305038 absolute error = 0.1600522904254855 relative error = 13.07351217775867 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -1.395000000000056 y[1] (analytic) = 1.247833036367215 y[1] (numeric) = 1.066027878193912 absolute error = 0.1818051581733027 relative error = 14.56967021025405 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -1.295000000000058 y[1] (analytic) = 1.27389786433143 y[1] (numeric) = 1.067859442082787 absolute error = 0.2060384222486431 relative error = 16.17385726262888 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -1.19500000000006 y[1] (analytic) = 1.302703954182125 y[1] (numeric) = 1.069691005971661 absolute error = 0.2330129482104637 relative error = 17.88686888240513 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -1.095000000000062 y[1] (analytic) = 1.334539606948587 y[1] (numeric) = 1.071522569860536 absolute error = 0.2630170370880514 relative error = 19.70844744648962 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -0.9950000000000639 y[1] (analytic) = 1.369723444544035 y[1] (numeric) = 1.07335413374941 absolute error = 0.2963693107946255 relative error = 21.63716420092987 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -0.8950000000000639 y[1] (analytic) = 1.408607598640822 y[1] (numeric) = 1.075185697638284 absolute error = 0.3334219010025381 relative error = 23.67031821525454 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -0.7950000000000638 y[1] (analytic) = 1.451581234922563 y[1] (numeric) = 1.077017261527159 absolute error = 0.3745639733954047 relative error = 25.80385888051152 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -0.6950000000000637 y[1] (analytic) = 1.499074447985104 y[1] (numeric) = 1.078848825416033 absolute error = 0.420225622569071 relative error = 28.03233842948183 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -0.5950000000000636 y[1] (analytic) = 1.551562565867795 y[1] (numeric) = 1.080680389304908 absolute error = 0.4708821765628872 relative error = 30.3489003229155 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -0.4950000000000635 y[1] (analytic) = 1.609570907296271 y[1] (numeric) = 1.082511953193782 absolute error = 0.5270589541024888 relative error = 32.74530818824461 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -0.3950000000000634 y[1] (analytic) = 1.673680039248825 y[1] (numeric) = 1.084343517082656 absolute error = 0.5893365221661686 relative error = 35.21201832762925 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -0.2950000000000633 y[1] (analytic) = 1.744531587465862 y[1] (numeric) = 1.086175080971531 absolute error = 0.6583565064943315 relative error = 37.73829669949811 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -0.1950000000000632 y[1] (analytic) = 1.822834658055966 y[1] (numeric) = 1.088006644860405 absolute error = 0.7348280131955613 relative error = 40.31237885169725 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = -0.09500000000006315 y[1] (analytic) = 1.909372934468174 y[1] (numeric) = 1.08983820874928 absolute error = 0.8195347257188945 relative error = 42.92166872822899 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.004999999999936872 y[1] (analytic) = 2.005012520859338 y[1] (numeric) = 1.091669772638154 absolute error = 0.9133427482211838 relative error = 45.55296980538206 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1049999999999369 y[1] (analytic) = 2.110710610355635 y[1] (numeric) = 1.093501336527028 absolute error = 1.017209273828607 relative error = 48.19273986864626 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.204999999999937 y[1] (analytic) = 2.227525064963101 y[1] (numeric) = 1.095332900415903 absolute error = 1.132192164547198 relative error = 50.82735913303642 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.304999999999937 y[1] (analytic) = 2.356625003006139 y[1] (numeric) = 1.097164464304777 absolute error = 1.259460538701362 relative error = 53.44340050261619 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4049999999999371 y[1] (analytic) = 2.499302500056673 y[1] (numeric) = 1.098996028193651 absolute error = 1.400306471863021 relative error = 56.02789065474342 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5049999999999372 y[1] (analytic) = 2.656985520460747 y[1] (numeric) = 1.100827592082526 absolute error = 1.556157928378221 relative error = 58.5685513298683 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6049999999999373 y[1] (analytic) = 2.831252208885658 y[1] (numeric) = 1.1026591559714 absolute error = 1.728593052914258 relative error = 61.05401163093867 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7049999999999373 y[1] (analytic) = 3.023846684922221 y[1] (numeric) = 1.104490719860275 absolute error = 1.919355965061946 relative error = 63.47398413525439 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8049999999999374 y[1] (analytic) = 3.236696498819847 y[1] (numeric) = 1.106322283749149 absolute error = 2.130374215070698 relative error = 65.81939999154902 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9049999999999375 y[1] (analytic) = 3.471931923057317 y[1] (numeric) = 1.108153847638023 absolute error = 2.363778075419294 relative error = 68.08250068848687 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.004999999999937 y[1] (analytic) = 3.731907272825756 y[1] (numeric) = 1.109985411526898 absolute error = 2.621921861298858 relative error = 70.2568866164129 % Correct digits = 0 h = 0.005 Finished! diff ( y , x , 2 ) = diff ( y , x , 1 ) ; Iterations = 1001 Total Elapsed Time Unknown Elapsed Time(since restart) Unknown Time to Timeout = 25 Minutes 31 Seconds Percent Done = 100.2 %