##############ECHO OF PROBLEM################# ##############temp/add_full_linpostode.ode################# diff ( y , x , 1 ) = sin(0.3 * x + 0.1) + (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(0.05 * x * x + 0.2 * x - cos(0.3 * x + 0.1) / 0.3); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = -3.284706312382627 y[1] (numeric) = -3.284706312382627 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) = -3.24875761125209 y[1] (numeric) = -3.248757611252089 absolute error = 4.440892098500626e-16 relative error = 1.366950887046658e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = -3.208847450390901 y[1] (numeric) = -3.2088474503909 absolute error = 8.881784197001252e-16 relative error = 2.767904780241041e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = -3.164991497768685 y[1] (numeric) = -3.164991497768684 absolute error = 8.881784197001252e-16 relative error = 2.806258469655574e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = -3.117208072368816 y[1] (numeric) = -3.117208072368814 absolute error = 1.77635683940025e-15 relative error = 5.698550748491963e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = -3.06551812770257 y[1] (numeric) = -3.065518127702568 absolute error = 1.332267629550188e-15 relative error = 4.345978637381754e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = -3.009945232952378 y[1] (numeric) = -3.009945232952376 absolute error = 1.77635683940025e-15 relative error = 5.901625119131712e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = -2.950515551761154 y[1] (numeric) = -2.950515551761152 absolute error = 1.77635683940025e-15 relative error = 6.02049644625648e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = -2.887257818686781 y[1] (numeric) = -2.88725781868678 absolute error = 8.881784197001252e-16 relative error = 3.076200587116594e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = -2.82020331334295 y[1] (numeric) = -2.820203313342948 absolute error = 1.77635683940025e-15 relative error = 6.298683612617389e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = -2.745746820398183 y[1] (numeric) = -2.74574682039818 absolute error = 3.108624468950438e-15 relative error = 1.132159908501554e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = -2.67101730851976 y[1] (numeric) = -2.671017308519755 absolute error = 4.884981308350689e-15 relative error = 1.828884183104705e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = -2.592601841394378 y[1] (numeric) = -2.592601841394372 absolute error = 5.773159728050814e-15 relative error = 2.226782237007839e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = -2.510541694846624 y[1] (numeric) = -2.510541694846617 absolute error = 7.105427357601002e-15 relative error = 2.830236746191579e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = -2.424880524734055 y[1] (numeric) = -2.424880524734047 absolute error = 7.993605777301127e-15 relative error = 3.296494691497353e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = -2.335664327659871 y[1] (numeric) = -2.33566432765986 absolute error = 1.06581410364015e-14 relative error = 4.563216088109723e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = -2.242941399579079 y[1] (numeric) = -2.242941399579066 absolute error = 1.243449787580175e-14 relative error = 5.543835375340288e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = -2.146762292335393 y[1] (numeric) = -2.146762292335379 absolute error = 1.376676550535194e-14 relative error = 6.412803855603187e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = -2.047179768167986 y[1] (numeric) = -2.04717976816797 absolute error = 1.643130076445232e-14 relative error = 8.026310644500276e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = -1.944248752229038 y[1] (numeric) = -1.944248752229019 absolute error = 1.865174681370263e-14 relative error = 9.59329241812233e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = -1.838026283154803 y[1] (numeric) = -1.838026283154782 absolute error = 2.131628207280301e-14 relative error = 1.159737609204128e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = -1.728571461734689 y[1] (numeric) = -1.728571461734665 absolute error = 2.375877272697835e-14 relative error = 1.374474428909956e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = -1.615945397724537 y[1] (numeric) = -1.61594539772451 absolute error = 2.620126338115369e-14 relative error = 1.621420093652206e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = -1.500211154851962 y[1] (numeric) = -1.500211154851934 absolute error = 2.842170943040401e-14 relative error = 1.8945139381535e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = -1.381433694063261 y[1] (numeric) = -1.38143369406323 absolute error = 3.130828929442941e-14 relative error = 2.266362072170197e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = -1.25967981506294 y[1] (numeric) = -1.259679815062906 absolute error = 3.352873534367973e-14 relative error = 2.66168711626172e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = -1.135018096198491 y[1] (numeric) = -1.135018096198454 absolute error = 3.61932706027801e-14 relative error = 3.188783573055091e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = -1.007518832744509 y[1] (numeric) = -1.00751883274447 absolute error = 3.885780586188048e-14 relative error = 3.856782086745787e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = -0.8772539736416907 y[1] (numeric) = -0.877253973641649 absolute error = 4.163336342344337e-14 relative error = 4.745873449921616e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = -0.7442970567476401 y[1] (numeric) = -0.7442970567475957 absolute error = 4.440892098500626e-14 relative error = 5.9665587257674e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = -0.6087231426577639 y[1] (numeric) = -0.6087231426577164 absolute error = 4.75175454539567e-14 relative error = 7.806101349537813e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = -0.4706087471558011 y[1] (numeric) = -0.4706087471557507 absolute error = 5.040412531798211e-14 relative error = 1.07104097878774e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = -0.3300317723547821 y[1] (numeric) = -0.3300317723547286 absolute error = 5.35682609381638e-14 relative error = 1.623124360298809e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = -0.1870714365903851 y[1] (numeric) = -0.1870714365903285 absolute error = 5.65381075290361e-14 relative error = 3.022273659705353e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = -0.04180820312978151 y[1] (numeric) = -0.04180820312972183 absolute error = 5.968142646750607e-14 relative error = 1.427505178403441e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 0.1056762922398738 y[1] (numeric) = 0.1056762922399365 absolute error = 6.26859675278979e-14 relative error = 5.931885591293032e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 0.25529931467814 y[1] (numeric) = 0.255299314678206 absolute error = 6.605826996519681e-14 relative error = 2.587483246810809e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 0.4069771047470637 y[1] (numeric) = 0.4069771047471329 absolute error = 6.922240558537851e-14 relative error = 1.700891887478541e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 0.5606249537890178 y[1] (numeric) = 0.5606249537890903 absolute error = 7.249756350802272e-14 relative error = 1.293156200380371e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 0.7161572801587769 y[1] (numeric) = 0.7161572801588526 absolute error = 7.571721027943568e-14 relative error = 1.057270691469458e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 0.8734877062412209 y[1] (numeric) = 0.8734877062413001 absolute error = 7.926992395823618e-14 relative error = 9.075104708611106e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 1.032529136185358 y[1] (numeric) = 1.032529136185441 absolute error = 8.282263763703668e-14 relative error = 8.021336612642421e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 1.193193834284713 y[1] (numeric) = 1.193193834284799 absolute error = 8.593126210598712e-14 relative error = 7.201785630873672e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 1.355393503933541 y[1] (numeric) = 1.35539350393363 absolute error = 8.903988657493755e-14 relative error = 6.569301558295168e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 1.519039367087808 y[1] (numeric) = 1.519039367087901 absolute error = 9.259260025373806e-14 relative error = 6.09547074683455e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 1.684042244159448 y[1] (numeric) = 1.684042244159545 absolute error = 9.636735853746359e-14 relative error = 5.722383679606754e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 1.850312634271964 y[1] (numeric) = 1.850312634272063 absolute error = 9.925393840148899e-14 relative error = 5.364171252094492e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 2.017760795805178 y[1] (numeric) = 2.017760795805281 absolute error = 1.030286966852145e-13 relative error = 5.106090716967341e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 2.186296827156634 y[1] (numeric) = 2.186296827156741 absolute error = 1.06581410364015e-13 relative error = 4.874974387747174e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 2.355830747646971 y[1] (numeric) = 2.355830747647082 absolute error = 1.110223024625157e-13 relative error = 4.712660388417373e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = sin(0.3 * x + 0.1) + (0.1 * x + 0.2) ; Iterations = 981 Total Elapsed Time = 49 Seconds Elapsed Time(since restart) = 48 Seconds Time to Timeout = 9 Minutes 11 Seconds Percent Done = 100.2 %