##############ECHO OF PROBLEM################# ##############temp/sing5_back_sm_hpostode.ode################# diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=20; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-0.7; x_end=-1.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.000001; glob_type_given_pole=1; array_given_rad_poles[1][1]=0.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=4.0; array_given_ord_poles[1][2]=0.0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(1.0/x/x/x); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.3 estimated_steps = 300000.0000000001 step_error = 9.128709291752769e-15 est_needed_step_err = 9.128709291752769e-15 opt_iter = 1 SETTING H FOR MAX H Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = -0.7 y[1] (analytic) = -2.915451895043732 y[1] (numeric) = -2.915451895043732 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = -1e-06 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7100000000002875 y[1] (analytic) = -2.793990684831662 y[1] (numeric) = -2.793990684835157 absolute error = 3.494982081519993e-12 relative error = 1.250892531780422e-10 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 12 h = -1e-06 Radius of convergence (given) for eq 1 = 0.71 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.71 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7200000000005751 y[1] (analytic) = -2.679183813436653 y[1] (numeric) = -2.679183813443464 absolute error = 6.81144030068026e-12 relative error = 2.542356469354398e-10 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 12 h = -1e-06 Radius of convergence (given) for eq 1 = 0.72 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.72 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7300000000008626 y[1] (analytic) = -2.570581748346358 y[1] (numeric) = -2.570581748356314 absolute error = 9.956035995628554e-12 relative error = 3.873067254925163e-10 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 12 h = -1e-06 Radius of convergence (given) for eq 1 = 0.73 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.73 Order of pole (three term test) = 4.157e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7400000000011502 y[1] (analytic) = -2.4677709118792 y[1] (numeric) = -2.467770911892123 absolute error = 1.292299600663682e-11 relative error = 5.236708133817818e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = -1e-06 Radius of convergence (given) for eq 1 = 0.74 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.74 Order of pole (three term test) = 6.425e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7500000000014377 y[1] (analytic) = -2.370370370356738 y[1] (numeric) = -2.370370370372465 absolute error = 1.572608709921042e-11 relative error = 6.63444299501755e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = -1e-06 Radius of convergence (given) for eq 1 = 0.75 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.75 Order of pole (three term test) = 2.468e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7600000000017253 y[1] (analytic) = -2.27802886716629 y[1] (numeric) = -2.278028867184669 absolute error = 1.837907603885469e-11 relative error = 8.067973283287225e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = -1e-06 Radius of convergence (given) for eq 1 = 0.76 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.76 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7700000000020129 y[1] (analytic) = -2.190422160045731 y[1] (numeric) = -2.190422160066656 absolute error = 2.09250394789251e-11 relative error = 9.552971048507028e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = -1e-06 Radius of convergence (given) for eq 1 = 0.77 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.77 Order of pole (three term test) = 2.865e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7800000000023004 y[1] (analytic) = -2.107250627942043 y[1] (numeric) = -2.107250627965369 absolute error = 2.332622983658439e-11 relative error = 1.106950902150873e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.78 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.78 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.790000000002588 y[1] (analytic) = -2.028237117124958 y[1] (numeric) = -2.028237117150525 absolute error = 2.55671039894878e-11 relative error = 1.260557938399696e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.79 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.79 Order of pole (three term test) = 3.254e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8000000000028755 y[1] (analytic) = -1.953124999978939 y[1] (numeric) = -1.95312500000666 absolute error = 2.772049256805076e-11 relative error = 1.419289219499503e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.8 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8100000000031631 y[1] (analytic) = -1.881676423136877 y[1] (numeric) = -1.881676423166659 absolute error = 2.978217672477967e-11 relative error = 1.582746978097906e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.81 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.81 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8200000000034506 y[1] (analytic) = -1.813670724429738 y[1] (numeric) = -1.813670724461462 absolute error = 3.172462292866385e-11 relative error = 1.749194189515235e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.82 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.82 Order of pole (three term test) = 5.363e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8300000000037382 y[1] (analytic) = -1.748903000569248 y[1] (numeric) = -1.748903000602821 absolute error = 3.357314426466473e-11 relative error = 1.919668743991923e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.83 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.83 Order of pole (three term test) = 3.952e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8400000000040257 y[1] (analytic) = -1.687182809607531 y[1] (numeric) = -1.687182809642887 absolute error = 3.535549630839796e-11 relative error = 2.095534408427399e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.84 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.84 Order of pole (three term test) = 2.899e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8500000000043133 y[1] (analytic) = -1.628332994072504 y[1] (numeric) = -1.628332994109558 absolute error = 3.705413753607445e-11 relative error = 2.275587221468815e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.85 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.85 Order of pole (three term test) = 4.233e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8600000000046009 y[1] (analytic) = -1.57218861229821 y[1] (numeric) = -1.572188612336882 absolute error = 3.867106634913853e-11 relative error = 2.459696377816242e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.86 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.86 Order of pole (three term test) = 6.155e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8700000000048884 y[1] (analytic) = -1.518595966887233 y[1] (numeric) = -1.518595966927449 absolute error = 4.021583066560197e-11 relative error = 2.648224514123729e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.87 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.87 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.880000000005176 y[1] (analytic) = -1.467411720485001 y[1] (numeric) = -1.467411720526693 absolute error = 4.169176115453865e-11 relative error = 2.84117678580071e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.88 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.88 Order of pole (three term test) = 3.211e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8900000000054635 y[1] (analytic) = -1.418502090136706 y[1] (numeric) = -1.418502090179807 absolute error = 4.310107826199783e-11 relative error = 3.038492404184193e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.89 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.89 Order of pole (three term test) = 4.61e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9000000000057511 y[1] (analytic) = -1.371742112456557 y[1] (numeric) = -1.371742112501011 absolute error = 4.445377399520112e-11 relative error = 3.240680124312286e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.9 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9 Order of pole (three term test) = 3.296e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9100000000060386 y[1] (analytic) = -1.327014972683519 y[1] (numeric) = -1.327014972729266 absolute error = 4.574651768507465e-11 relative error = 3.447324907914567e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.91 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.91 Order of pole (three term test) = 2.347e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9200000000063262 y[1] (analytic) = -1.284211391442235 y[1] (numeric) = -1.284211391489217 absolute error = 4.698219591148245e-11 relative error = 3.658447217067514e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.92 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.92 Order of pole (three term test) = 3.329e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9300000000066138 y[1] (analytic) = -1.243229063685236 y[1] (numeric) = -1.243229063733396 absolute error = 4.815969845139989e-11 relative error = 3.873759056809911e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.93 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.93 Order of pole (three term test) = 2.353e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9400000000069013 y[1] (analytic) = -1.203972144873938 y[1] (numeric) = -1.20397214492322 absolute error = 4.92828000631107e-11 relative error = 4.093350520852031e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.94 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.94 Order of pole (three term test) = 3.313e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9500000000071889 y[1] (analytic) = -1.166350779970606 y[1] (numeric) = -1.166350780020962 absolute error = 5.035594163871338e-11 relative error = 4.317392546347199e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.95 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.95 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9600000000074764 y[1] (analytic) = -1.130280671269889 y[1] (numeric) = -1.130280671321293 absolute error = 5.140488035237922e-11 relative error = 4.547974822450517e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.96 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.96 Order of pole (three term test) = 3.249e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.970000000007764 y[1] (analytic) = -1.095682681503658 y[1] (numeric) = -1.095682681556066 absolute error = 5.240852196664036e-11 relative error = 4.783184297000812e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.97 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.97 Order of pole (three term test) = 4.527e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9800000000080515 y[1] (analytic) = -1.062482469013073 y[1] (numeric) = -1.062482469066436 absolute error = 5.33624255893983e-11 relative error = 5.022428806657486e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.98 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.98 Order of pole (three term test) = 3.143e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9900000000083391 y[1] (analytic) = -1.030610152102321 y[1] (numeric) = -1.0306101521566 absolute error = 5.427946980773868e-11 relative error = 5.266731527630994e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-06 Radius of convergence (given) for eq 1 = 0.99 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.99 Order of pole (three term test) = 4.349e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; Iterations = 300000 Total Elapsed Time = 9.0 Seconds Elapsed Time(since restart) = 9.0 Seconds Expected Time Remaining = 0.0 Seconds Optimized Time Remaining = 0.0 Seconds Expected Total Time = 9.0 Seconds Time to Timeout = 9 Minutes 51.0 Seconds Percent Done = 0 %