##############ECHO OF PROBLEM################# ##############temp/sing1postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=20; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=-2.0; x_end=-1.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.0000001; glob_type_given_pole=2; array_given_rad_poles[1][1]=0.0; array_given_rad_poles[1][2]=0.001; array_given_ord_poles[1][1]=1.0; 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) { } // 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 = 0.5 estimated_steps = 500000 step_error = 7.071067811865475e-15 est_needed_step_err = 7.071067811865475e-15 opt_iter = 1 SETTING H FOR MAX H Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 0.2 Order of pole (six term test) = 1 START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (analytic) = -2 y[1] (numeric) = -2 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 1e-07 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 2 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.989999999994161 y[1] (analytic) = -1.989999999994161 y[1] (numeric) = -1.997481125479834 absolute error = 0.007481125485672813 relative error = 0.3759359540550132 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.99 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.99 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.979999999988323 y[1] (analytic) = -1.979999999988323 y[1] (numeric) = -1.994923989911978 absolute error = 0.01492398992365573 relative error = 0.7537368648355429 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.98 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.98 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.98 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.969999999982484 y[1] (analytic) = -1.969999999982484 y[1] (numeric) = -1.992327814454274 absolute error = 0.02232781447179044 relative error = 1.133391597562892 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.97 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.97 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.97 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.959999999976645 y[1] (analytic) = -1.959999999976645 y[1] (numeric) = -1.989691800345517 absolute error = 0.02969180036887198 relative error = 1.514887773940091 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.96 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.96 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.96 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.949999999970807 y[1] (analytic) = -1.949999999970807 y[1] (numeric) = -1.987015128291221 absolute error = 0.03701512832041387 relative error = 1.898211708767591 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.95 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.95 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.939999999964968 y[1] (analytic) = -1.939999999964968 y[1] (numeric) = -1.984296957826646 absolute error = 0.04429695786167787 relative error = 2.283348343426689 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.94 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.94 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.94 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.929999999959129 y[1] (analytic) = -1.929999999959129 y[1] (numeric) = -1.981536426657085 absolute error = 0.05153642669795522 relative error = 2.670281176116403 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.93 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.93 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.93 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.919999999953291 y[1] (analytic) = -1.919999999953291 y[1] (numeric) = -1.97873264997406 absolute error = 0.05873265002076944 relative error = 3.05899218865616 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.92 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.92 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.92 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.909999999947452 y[1] (analytic) = -1.909999999947452 y[1] (numeric) = -1.975884719745912 absolute error = 0.06588471979845956 relative error = 3.449461769647758 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.91 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.91 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.91 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.899999999941613 y[1] (analytic) = -1.899999999941613 y[1] (numeric) = -1.97299170398293 absolute error = 0.07299170404131639 relative error = 3.841668633871548 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.9 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.9 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.889999999935775 y[1] (analytic) = -1.889999999935775 y[1] (numeric) = -1.970052645974393 absolute error = 0.08005264603861884 relative error = 4.235589737636992 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.89 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.89 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.89 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.879999999929936 y[1] (analytic) = -1.879999999929936 y[1] (numeric) = -1.967066563497751 absolute error = 0.08706656356781539 relative error = 4.631200189950011 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.88 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.88 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.88 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.869999999924097 y[1] (analytic) = -1.869999999924097 y[1] (numeric) = -1.964032447997716 absolute error = 0.09403244807361921 relative error = 5.028473159221175 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.87 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.87 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.859999999918259 y[1] (analytic) = -1.859999999918259 y[1] (numeric) = -1.960949263734651 absolute error = 0.100949263816392 relative error = 5.427379775313357 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.86 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.86 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.86 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.84999999991242 y[1] (analytic) = -1.84999999991242 y[1] (numeric) = -1.957815946900553 absolute error = 0.1078159469881328 relative error = 5.827889026661452 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.85 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.85 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.839999999906581 y[1] (analytic) = -1.839999999906581 y[1] (numeric) = -1.954631404701227 absolute error = 0.114631404794646 relative error = 6.229967652199234 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.84 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.84 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.829999999900743 y[1] (analytic) = -1.829999999900743 y[1] (numeric) = -1.951394514403334 absolute error = 0.1213945145025914 relative error = 6.63358002782381 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.83 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.83 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.83 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.819999999894904 y[1] (analytic) = -1.819999999894904 y[1] (numeric) = -1.948104122344922 absolute error = 0.1281041224500186 relative error = 7.038688047110766 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.82 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.82 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.82 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.809999999889065 y[1] (analytic) = -1.809999999889065 y[1] (numeric) = -1.944759042906925 absolute error = 0.13475904301786 relative error = 7.445250995918198 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.81 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.81 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.81 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.799999999883227 y[1] (analytic) = -1.799999999883227 y[1] (numeric) = -1.941358057445277 absolute error = 0.1413580575620503 relative error = 7.853225420623379 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.8 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.789999999877388 y[1] (analytic) = -1.789999999877388 y[1] (numeric) = -1.937899913180826 absolute error = 0.1478999133034378 relative error = 8.262564989584842 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.79 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.79 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.79 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.779999999871549 y[1] (analytic) = -1.779999999871549 y[1] (numeric) = -1.934383322045327 absolute error = 0.1543833221737783 relative error = 8.673220347467364 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.78 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.78 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.78 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.769999999865711 y[1] (analytic) = -1.769999999865711 y[1] (numeric) = -1.930806959482056 absolute error = 0.1608069596163451 relative error = 9.085138962064713 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.77 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.77 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.77 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.759999999859872 y[1] (analytic) = -1.759999999859872 y[1] (numeric) = -1.927169463198229 absolute error = 0.1671694633383576 relative error = 9.498264963162915 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.76 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.76 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.76 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.749999999854033 y[1] (analytic) = -1.749999999854033 y[1] (numeric) = -1.923469431867477 absolute error = 0.1734694320134442 relative error = 9.912538973023615 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 3 h = 1e-07 Radius of convergence (given) for eq 1 = 1.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.75 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.75 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.739999999848195 y[1] (analytic) = -1.739999999848195 y[1] (numeric) = -1.919705423780186 absolute error = 0.1797054239319911 relative error = 10.32789792802698 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.74 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.74 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.74 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.729999999842356 y[1] (analytic) = -1.729999999842356 y[1] (numeric) = -1.915875955438667 absolute error = 0.185875955596311 relative error = 10.74427489093923 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.73 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.73 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.73 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.719999999836517 y[1] (analytic) = -1.719999999836517 y[1] (numeric) = -1.911979500095432 absolute error = 0.1919795002589149 relative error = 11.16159885332338 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.72 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.72 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.709999999830679 y[1] (analytic) = -1.709999999830679 y[1] (numeric) = -1.908014486231053 absolute error = 0.1980144864003743 relative error = 11.57979452748429 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.71 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.71 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.71 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.69999999982484 y[1] (analytic) = -1.69999999982484 y[1] (numeric) = -1.90397929596942 absolute error = 0.2039792961445797 relative error = 11.99878212738804 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.7 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.7 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.689999999819001 y[1] (analytic) = -1.689999999819001 y[1] (numeric) = -1.899872263427122 absolute error = 0.2098722636081207 relative error = 12.41847713790521 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.69 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.69 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.69 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.679999999813163 y[1] (analytic) = -1.679999999813163 y[1] (numeric) = -1.895691672993817 absolute error = 0.2156916731806549 relative error = 12.83879007170491 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.68 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.68 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.68 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.669999999807324 y[1] (analytic) = -1.669999999807324 y[1] (numeric) = -1.891435757540256 absolute error = 0.221435757732932 relative error = 13.25962621308264 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.67 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.67 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.67 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.659999999801485 y[1] (analytic) = -1.659999999801485 y[1] (numeric) = -1.887102696550587 absolute error = 0.2271026967491014 relative error = 13.68088534796747 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.66 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.66 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.66 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.649999999795646 y[1] (analytic) = -1.649999999795646 y[1] (numeric) = -1.882690614175179 absolute error = 0.2326906143795326 relative error = 14.10246147929403 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.65 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.65 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.639999999789808 y[1] (analytic) = -1.639999999789808 y[1] (numeric) = -1.878197577200085 absolute error = 0.2381975774102771 relative error = 14.52424252687841 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.64 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.64 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.629999999783969 y[1] (analytic) = -1.629999999783969 y[1] (numeric) = -1.873621592929041 absolute error = 0.243621593145072 relative error = 14.946110010881 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.63 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.63 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.63 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.61999999977813 y[1] (analytic) = -1.61999999977813 y[1] (numeric) = -1.868960606973522 absolute error = 0.2489606071953911 relative error = 15.36793871786963 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.62 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.62 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.62 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.609999999772292 y[1] (analytic) = -1.609999999772292 y[1] (numeric) = -1.864212500946709 absolute error = 0.2542125011744172 relative error = 15.78959634847027 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.61 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.61 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.61 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.599999999766453 y[1] (analytic) = -1.599999999766453 y[1] (numeric) = -1.859375090055936 absolute error = 0.2593750902894827 relative error = 16.21094314545893 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.6 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.589999999760614 y[1] (analytic) = -1.589999999760614 y[1] (numeric) = -1.854446120589155 absolute error = 0.2644461208285407 relative error = 16.63183150115439 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.59 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.59 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.59 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.579999999754776 y[1] (analytic) = -1.579999999754776 y[1] (numeric) = -1.849423267289218 absolute error = 0.2694232675344421 relative error = 17.05210554280114 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.58 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.58 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.58 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.569999999748937 y[1] (analytic) = -1.569999999748937 y[1] (numeric) = -1.844304130611299 absolute error = 0.2743041308623622 relative error = 17.47160069466413 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.57 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.57 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.57 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.559999999743098 y[1] (analytic) = -1.559999999743098 y[1] (numeric) = -1.839086233856408 absolute error = 0.2790862341133091 relative error = 17.89014321533777 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.56 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.56 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.56 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.54999999973726 y[1] (analytic) = -1.54999999973726 y[1] (numeric) = -1.833767020175151 absolute error = 0.2837670204378913 relative error = 18.30754970877371 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.55 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.55 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.539999999731421 y[1] (analytic) = -1.539999999731421 y[1] (numeric) = -1.828343849434916 absolute error = 0.2883438497034947 relative error = 18.72362660738847 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.54 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.54 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.54 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.529999999725582 y[1] (analytic) = -1.529999999725582 y[1] (numeric) = -1.822813994943424 absolute error = 0.2928139952178415 relative error = 19.13816962551372 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.53 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.53 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.53 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.519999999719744 y[1] (analytic) = -1.519999999719744 y[1] (numeric) = -1.817174640020368 absolute error = 0.2971746403006243 relative error = 19.55096318127744 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.52 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.52 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.52 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.509999999713905 y[1] (analytic) = -1.509999999713905 y[1] (numeric) = -1.81142287441022 absolute error = 0.301422874696315 relative error = 19.96177978499501 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 2 h = 1e-07 Radius of convergence (given) for eq 1 = 1.51 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.51 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.51 Order of pole (six term test) = 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; Iterations = 5000000 Total Elapsed Time = 24.0 Seconds Elapsed Time(since restart) = 24.0 Seconds Time to Timeout = 9 Minutes 36.0 Seconds Percent Done = 100 %