##############ECHO OF PROBLEM################# ##############temp/add_sin_cpostode.ode################# diff ( y , x , 1 ) = sin ( x ) + 1.0 ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=-5.0; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=16; glob_max_minutes=3.0; glob_subiter_method=3; glob_max_iter=100000000; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(2.0 - cos(x) + x); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 10000000 step_error = 7.905694150420948e-22 est_needed_step_err = 7.905694150420948e-22 opt_iter = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 3.283662185463226 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 3.283662185463226 desired_abs_gbl_error = 3.283662185463226e-16 range = 10 estimated_steps = 10000000 step_error = 2.595962893157509e-21 est_needed_step_err = 2.595962893157509e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.625464009062711e-259 estimated_step_error = 7.625464009062711e-259 Double H and LOOP opt_iter = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 3.283662185463226 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 3.283662185463226 desired_abs_gbl_error = 3.283662185463226e-16 range = 10 estimated_steps = 5000000 step_error = 3.671245930920648e-21 est_needed_step_err = 3.671245930920648e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.240178726334705e-248 estimated_step_error = 5.240178726334705e-248 Double H and LOOP opt_iter = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 3.283662185463226 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 3.283662185463226 desired_abs_gbl_error = 3.283662185463226e-16 range = 10 estimated_steps = 2500000 step_error = 5.191925786315018e-21 est_needed_step_err = 5.191925786315018e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.601023071759884e-237 estimated_step_error = 3.601023071759884e-237 Double H and LOOP opt_iter = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 3.283662185463226 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 3.283662185463226 desired_abs_gbl_error = 3.283662185463226e-16 range = 10 estimated_steps = 1250000 step_error = 7.342491861841295e-21 est_needed_step_err = 7.342491861841295e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.474603759870156e-226 estimated_step_error = 2.474603759870156e-226 Double H and LOOP opt_iter = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 3.283662185463226 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 3.283662185463226 desired_abs_gbl_error = 3.283662185463226e-16 range = 10 estimated_steps = 625000 step_error = 1.038385157263004e-20 est_needed_step_err = 1.038385157263004e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.700534133592597e-215 estimated_step_error = 1.700534133592597e-215 Double H and LOOP opt_iter = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 3.283662185463226 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 3.283662185463226 desired_abs_gbl_error = 3.283662185463226e-16 range = 10 estimated_steps = 312500 step_error = 1.468498372368259e-20 est_needed_step_err = 1.468498372368259e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.168597304166826e-204 estimated_step_error = 1.168597304166826e-204 Double H and LOOP opt_iter = 7 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 3.283662185463226 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 3.283662185463226 desired_abs_gbl_error = 3.283662185463226e-16 range = 10 estimated_steps = 156250 step_error = 2.076770314526007e-20 est_needed_step_err = 2.076770314526007e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.030527786324255e-194 estimated_step_error = 8.030527786324255e-194 Double H and LOOP opt_iter = 8 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 3.283662185463226 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 3.283662185463226 desired_abs_gbl_error = 3.283662185463226e-16 range = 10 estimated_steps = 78125 step_error = 2.936996744736518e-20 est_needed_step_err = 2.936996744736518e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.518520539358821e-183 estimated_step_error = 5.518520539358821e-183 Double H and LOOP opt_iter = 9 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.272 Order of pole (three term test) = 32.92 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (closed_form) = -3.283662185463226 y[1] (numeric) = -3.283662185463226 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.8999039999999 y[1] (closed_form) = -3.086322053112261 y[1] (numeric) = -3.086322053112453 absolute error = 1.922906278650771e-13 relative error = 6.23041356527166e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.7999359999998 y[1] (closed_form) = -2.887371228724927 y[1] (numeric) = -2.887371228725321 absolute error = 3.939071291370055e-13 relative error = 1.364241373669697e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.6999679999997 y[1] (closed_form) = -2.687547338998616 y[1] (numeric) = -2.687547338999208 absolute error = 5.919709167301335e-13 relative error = 2.20264368236469e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.5999999999996 y[1] (closed_form) = -2.487847473064148 y[1] (numeric) = -2.487847473064942 absolute error = 7.94475596421762e-13 relative error = 3.193425662238245e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.4999039999995 y[1] (closed_form) = -2.289014358648426 y[1] (numeric) = -2.289014358649423 absolute error = 9.969802761133906e-13 relative error = 4.355500315437376e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.3999359999994 y[1] (closed_form) = -2.092542228117139 y[1] (numeric) = -2.092542228118335 absolute error = 1.195488152916369e-12 relative error = 5.713089737701799e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.2999679999993 y[1] (closed_form) = -1.899139510813921 y[1] (numeric) = -1.899139510815312 absolute error = 1.391109449855321e-12 relative error = 7.324946071282189e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.1999999999992 y[1] (closed_form) = -1.709739178657803 y[1] (numeric) = -1.709739178659386 absolute error = 1.582955988510548e-12 relative error = 9.258464731171548e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.0999039999991 y[1] (closed_form) = -1.525001501511341 y[1] (numeric) = -1.525001501513109 absolute error = 1.767253010598324e-12 relative error = 1.158853292175058e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.999935999999 y[1] (closed_form) = -1.346243945113627 y[1] (numeric) = -1.34624394511557 absolute error = 1.943334382303874e-12 relative error = 1.443523210899085e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.8999679999989 y[1] (closed_form) = -1.17401368765259 y[1] (numeric) = -1.174013687654707 absolute error = 2.116529174145398e-12 relative error = 1.802814734108716e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.7999999999988 y[1] (closed_form) = -1.009032288083649 y[1] (numeric) = -1.009032288085929 absolute error = 2.280620137184997e-12 relative error = 2.260205311681694e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.6999039999987 y[1] (closed_form) = -0.8517531079261986 y[1] (numeric) = -0.8517531079286369 absolute error = 2.438271806681769e-12 relative error = 2.862650906690952e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.5999359999986 y[1] (closed_form) = -0.7031492641920432 y[1] (numeric) = -0.703149264194628 absolute error = 2.584821245932289e-12 relative error = 3.676063358897758e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.4999679999985 y[1] (closed_form) = -0.5635000881233587 y[1] (numeric) = -0.5635000881260834 absolute error = 2.724709347035059e-12 relative error = 4.835330826849097e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.3999999999984 y[1] (closed_form) = -0.4332018074185298 y[1] (numeric) = -0.4332018074213846 absolute error = 2.854827485521128e-12 relative error = 6.590063653088571e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.2999039999983 y[1] (closed_form) = -0.3124090910528592 y[1] (numeric) = -0.312409091055835 absolute error = 2.975786284054038e-12 relative error = 9.525287097200828e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.1999359999982 y[1] (closed_form) = -0.2016374903026725 y[1] (numeric) = -0.2016374903057597 absolute error = 3.087141653423942e-12 relative error = 1.531035547402379e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.0999679999981 y[1] (closed_form) = -0.1008341808176541 y[1] (numeric) = -0.1008341808208419 absolute error = 3.187866637333059e-12 relative error = 3.161494060330509e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.999999999998 y[1] (closed_form) = -0.01000750339783663 y[1] (numeric) = -0.01000750340111509 absolute error = 3.2784660403129e-12 relative error = 3.276007921238001e-08 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 10 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.8999039999979 y[1] (closed_form) = 0.07103119274144376 y[1] (numeric) = 0.0710311927380841 absolute error = 3.359659772605994e-12 relative error = 4.729837192563109e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.7999359999978 y[1] (closed_form) = 0.1422648994988545 y[1] (numeric) = 0.1422648994954237 absolute error = 3.430755679545427e-12 relative error = 2.411526449342519e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.6999679999977 y[1] (closed_form) = 0.2040904653993283 y[1] (numeric) = 0.2040904653958354 absolute error = 3.492928168924436e-12 relative error = 1.711460729970942e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.5999999999976 y[1] (closed_form) = 0.2568887533701103 y[1] (numeric) = 0.2568887533665649 absolute error = 3.545441717989206e-12 relative error = 1.380146725567678e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.4999039999975 y[1] (closed_form) = 0.3011821585305219 y[1] (numeric) = 0.3011821585269312 absolute error = 3.590683306242681e-12 relative error = 1.192196551004797e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.3999359999974 y[1] (closed_form) = 0.3374144843883813 y[1] (numeric) = 0.3374144843847539 absolute error = 3.627431688357774e-12 relative error = 1.075066974357395e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.2999679999973 y[1] (closed_form) = 0.3662841583725918 y[1] (numeric) = 0.3662841583689356 absolute error = 3.656186464695566e-12 relative error = 9.981830721099376e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.1999999999972 y[1] (closed_form) = 0.3885011172558821 y[1] (numeric) = 0.3885011172522034 absolute error = 3.678723992095456e-12 relative error = 9.469017793512559e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.0999039999971 y[1] (closed_form) = 0.404859234174852 y[1] (numeric) = 0.4048592341711577 absolute error = 3.69432262559144e-12 relative error = 9.124955821054393e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.999935999997 y[1] (closed_form) = 0.4161526406598683 y[1] (numeric) = 0.4161526406561625 absolute error = 3.705868945047541e-12 relative error = 8.905071319916093e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.899967999997073 y[1] (closed_form) = 0.4232912850953356 y[1] (numeric) = 0.4232912850916347 absolute error = 3.700928452587959e-12 relative error = 8.743219109163608e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.799999999997147 y[1] (closed_form) = 0.4272020946931618 y[1] (numeric) = 0.4272020946894641 absolute error = 3.697708805816546e-12 relative error = 8.655642965590859e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.69990399999722 y[1] (closed_form) = 0.428845293880175 y[1] (numeric) = 0.4288452938764792 absolute error = 3.695821426674684e-12 relative error = 8.618076214000251e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.599935999997294 y[1] (closed_form) = 0.4291995495309382 y[1] (numeric) = 0.429199549527243 absolute error = 3.695155292859909e-12 relative error = 8.609410929946815e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.499967999997367 y[1] (closed_form) = 0.4292628785289552 y[1] (numeric) = 0.4292628785252592 absolute error = 3.695932448977146e-12 relative error = 8.60995122998469e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.399999999997441 y[1] (closed_form) = 0.4300328570997962 y[1] (numeric) = 0.4300328570961005 absolute error = 3.695710404372221e-12 relative error = 8.594018674053481e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.299903999997514 y[1] (closed_form) = 0.4325046710224798 y[1] (numeric) = 0.4325046710187866 absolute error = 3.693212402566814e-12 relative error = 8.539127204882503e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.199935999997588 y[1] (closed_form) = 0.437646595764138 y[1] (numeric) = 0.4376465957604477 absolute error = 3.690270311551558e-12 relative error = 8.432078181959319e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.099967999997661 y[1] (closed_form) = 0.4464073601714011 y[1] (numeric) = 0.4464073601677173 absolute error = 3.683831018008732e-12 relative error = 8.252173567645255e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9999999999977344 y[1] (closed_form) = 0.4596976941322194 y[1] (numeric) = 0.4596976941285449 absolute error = 3.674505144601881e-12 relative error = 7.993307757478136e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8999039999977211 y[1] (closed_form) = 0.4784108352109994 y[1] (numeric) = 0.4784108352073221 absolute error = 3.677280702163443e-12 relative error = 7.686449452052246e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7999359999977078 y[1] (closed_form) = 0.5033113812905516 y[1] (numeric) = 0.5033113812868707 absolute error = 3.680944438144707e-12 relative error = 7.313453609386533e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6999679999976945 y[1] (closed_form) = 0.535169198141943 y[1] (numeric) = 0.535169198138257 absolute error = 3.68594044175552e-12 relative error = 6.887430096038332e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5999999999976813 y[1] (closed_form) = 0.5746643850913313 y[1] (numeric) = 0.5746643850876386 absolute error = 3.692712802205733e-12 relative error = 6.425859854911403e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.499903999997668 y[1] (closed_form) = 0.6224674173031066 y[1] (numeric) = 0.6224674172994067 absolute error = 3.699929251865797e-12 relative error = 5.943972566300831e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3999359999976547 y[1] (closed_form) = 0.6789780851109891 y[1] (numeric) = 0.6789780851072811 absolute error = 3.70803387994556e-12 relative error = 5.461198175990359e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2999679999976415 y[1] (closed_form) = 0.7446860547185763 y[1] (numeric) = 0.7446860547148599 absolute error = 3.716360552630249e-12 relative error = 4.99050644104608e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.199999999997639 y[1] (closed_form) = 0.8199334221606501 y[1] (numeric) = 0.8199334221569327 absolute error = 3.717470775654874e-12 relative error = 4.533869062025511e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.09990399999764472 y[1] (closed_form) = 0.9050822553010904 y[1] (numeric) = 0.9050822552973781 absolute error = 3.712363749741598e-12 relative error = 4.101686590360365e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.400000235686883e-05 y[1] (closed_form) = 1.000064002050357 y[1] (numeric) = 1.000064002046643 absolute error = 3.713696017371149e-12 relative error = 3.713458348422935e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1000320000023585 y[1] (closed_form) = 1.105031029903343 y[1] (numeric) = 1.105031029899625 absolute error = 3.717914864864724e-12 relative error = 3.364534356279508e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2000000000023528 y[1] (closed_form) = 1.219933422161579 y[1] (numeric) = 1.219933422157868 absolute error = 3.710587392902198e-12 relative error = 3.041631064035834e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000960000023552 y[1] (closed_form) = 1.344787885219432 y[1] (numeric) = 1.344787885215721 absolute error = 3.711031482112048e-12 relative error = 2.759566414079133e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000640000023685 y[1] (closed_form) = 1.47902793066063 y[1] (numeric) = 1.4790279306569 absolute error = 3.729239139715901e-12 relative error = 2.521412248144754e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5000320000023817 y[1] (closed_form) = 1.622464780179706 y[1] (numeric) = 1.622464780175958 absolute error = 3.747446797319753e-12 relative error = 2.309724588847274e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.600000000002395 y[1] (closed_form) = 1.774664385094069 y[1] (numeric) = 1.774664385090301 absolute error = 3.768318990182706e-12 relative error = 2.123398103795812e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000960000024082 y[1] (closed_form) = 1.935315661141744 y[1] (numeric) = 1.935315661137954 absolute error = 3.790079361465359e-12 relative error = 1.958377869597455e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8000640000024215 y[1] (closed_form) = 2.103403202873635 y[1] (numeric) = 2.103403202869822 absolute error = 3.812949955772638e-12 relative error = 1.812752757323678e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000320000024348 y[1] (closed_form) = 2.278447098513046 y[1] (numeric) = 2.278447098509203 absolute error = 3.842703932832592e-12 relative error = 1.686545162861322e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.000000000002448 y[1] (closed_form) = 2.459697694136368 y[1] (numeric) = 2.459697694132509 absolute error = 3.858691144387194e-12 relative error = 1.568766419379854e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.100096000002375 y[1] (closed_form) = 2.646585436575519 y[1] (numeric) = 2.646585436571797 absolute error = 3.721467578543525e-12 relative error = 1.406139218901931e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.200064000002301 y[1] (closed_form) = 2.837765896771342 y[1] (numeric) = 2.837765896767756 absolute error = 3.586464458749106e-12 relative error = 1.263833800677354e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.300032000002228 y[1] (closed_form) = 3.032564005378674 y[1] (numeric) = 3.032564005375231 absolute error = 3.443023643967535e-12 relative error = 1.135350692635293e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.400000000002154 y[1] (closed_form) = 3.230032857104036 y[1] (numeric) = 3.230032857100738 absolute error = 3.297806472346565e-12 relative error = 1.020982329976449e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.500096000002081 y[1] (closed_form) = 3.429454558180977 y[1] (numeric) = 3.429454558177827 absolute error = 3.150368854676344e-12 relative error = 9.186209647132157e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.600064000002007 y[1] (closed_form) = 3.629327494956053 y[1] (numeric) = 3.629327494953052 absolute error = 3.001154880166723e-12 relative error = 8.269176271189778e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.700032000001934 y[1] (closed_form) = 3.828908227507337 y[1] (numeric) = 3.828908227504485 absolute error = 2.851496816447252e-12 relative error = 7.447284309301948e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.80000000000186 y[1] (closed_form) = 4.027202094696759 y[1] (numeric) = 4.027202094694056 absolute error = 2.702726931147481e-12 relative error = 6.711177804328669e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.900096000001787 y[1] (closed_form) = 4.223476410185541 y[1] (numeric) = 4.223476410182993 absolute error = 2.548183886119659e-12 relative error = 6.033380179357306e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.000064000001713 y[1] (closed_form) = 4.416269030733422 y[1] (numeric) = 4.416269030731026 absolute error = 2.395417197931238e-12 relative error = 5.424074442161927e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.100032000001813 y[1] (closed_form) = 4.604905727044483 y[1] (numeric) = 4.60490572704191 absolute error = 2.573052881871263e-12 relative error = 5.587634219653608e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.200000000001913 y[1] (closed_form) = 4.788501117258805 y[1] (numeric) = 4.788501117256045 absolute error = 2.760458528427989e-12 relative error = 5.764765342705451e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.300096000002013 y[1] (closed_form) = 4.966443605913398 y[1] (numeric) = 4.966443605910459 absolute error = 2.938982390787714e-12 relative error = 5.917679981885539e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.400064000002113 y[1] (closed_form) = 5.13750094367813 y[1] (numeric) = 5.137500943675025 absolute error = 3.104183576851938e-12 relative error = 6.042205365765902e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.500032000002213 y[1] (closed_form) = 5.301194766248894 y[1] (numeric) = 5.301194766245626 absolute error = 3.268496584496461e-12 relative error = 6.165584794782473e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.600000000002313 y[1] (closed_form) = 5.456888753372453 y[1] (numeric) = 5.456888753369027 absolute error = 3.426592343203083e-12 relative error = 6.279388307275622e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.700096000002413 y[1] (closed_form) = 5.604209166322981 y[1] (numeric) = 5.604209166319402 absolute error = 3.579359031391505e-12 relative error = 6.386911917743399e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.800064000002513 y[1] (closed_form) = 5.742307777983937 y[1] (numeric) = 5.742307777980211 absolute error = 3.725908470642025e-12 relative error = 6.488521017503092e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.900032000002613 y[1] (closed_form) = 5.870997820634232 y[1] (numeric) = 5.870997820630389 absolute error = 3.842259843622742e-12 relative error = 6.544474995576937e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.000000000002713 y[1] (closed_form) = 5.989992496603541 y[1] (numeric) = 5.989992496599583 absolute error = 3.958611216603458e-12 relative error = 6.6087081391973e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.100096000002813 y[1] (closed_form) = 6.099235137415782 y[1] (numeric) = 6.09923513741171 absolute error = 4.072298054325074e-12 relative error = 6.676735627625742e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.200064000002913 y[1] (closed_form) = 6.198355037807811 y[1] (numeric) = 6.198355037803636 absolute error = 4.175326751010289e-12 relative error = 6.736185206465662e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.300032000003013 y[1] (closed_form) = 6.287506721543601 y[1] (numeric) = 6.287506721539338 absolute error = 4.263256414560601e-12 relative error = 6.780519852094821e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.400000000003113 y[1] (closed_form) = 6.366798192581779 y[1] (numeric) = 6.36679819257744 absolute error = 4.339639758654812e-12 relative error = 6.816047293145094e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.500096000003214 y[1] (closed_form) = 6.436519007787883 y[1] (numeric) = 6.43651900778346 absolute error = 4.423128530106624e-12 relative error = 6.871926463286828e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.600064000003314 y[1] (closed_form) = 6.496794093191081 y[1] (numeric) = 6.496794093186598 absolute error = 4.482636484226532e-12 relative error = 6.899766900300145e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.700032000003413 y[1] (closed_form) = 6.548115076521279 y[1] (numeric) = 6.54811507651676 absolute error = 4.519051799434237e-12 relative error = 6.901301743516406e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.800000000003513 y[1] (closed_form) = 6.590967711915781 y[1] (numeric) = 6.590967711911229 absolute error = 4.551914400963142e-12 relative error = 6.906291458132553e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.900096000003614 y[1] (closed_form) = 6.625962275304992 y[1] (numeric) = 6.625962275300408 absolute error = 4.583888824072346e-12 relative error = 6.918072626456888e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.000064000003714 y[1] (closed_form) = 6.653659184166186 y[1] (numeric) = 6.653659184161564 absolute error = 4.622080496119452e-12 relative error = 6.946674556338393e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.100032000003814 y[1] (closed_form) = 6.674829761372102 y[1] (numeric) = 6.674829761367464 absolute error = 4.638067707674054e-12 relative error = 6.948593257786153e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.200000000003913 y[1] (closed_form) = 6.690260821341202 y[1] (numeric) = 6.690260821336554 absolute error = 4.647837670290755e-12 relative error = 6.947169616264676e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.300096000004014 y[1] (closed_form) = 6.700807218303636 y[1] (numeric) = 6.700807218298982 absolute error = 4.654054919228656e-12 relative error = 6.945513827820387e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.400064000004114 y[1] (closed_form) = 6.707335966816514 y[1] (numeric) = 6.707335966811846 absolute error = 4.667377595524158e-12 relative error = 6.95861608634974e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.500032000004214 y[1] (closed_form) = 6.710796518359187 y[1] (numeric) = 6.710796518354518 absolute error = 4.669153952363558e-12 relative error = 6.957674755284016e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.600000000004314 y[1] (closed_form) = 6.712152526935082 y[1] (numeric) = 6.712152526930407 absolute error = 4.675371201301459e-12 relative error = 6.965531820887177e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.700096000004414 y[1] (closed_form) = 6.712388670773225 y[1] (numeric) = 6.712388670768555 absolute error = 4.670042130783258e-12 relative error = 6.957347614743082e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.800064000004514 y[1] (closed_form) = 6.712501262204847 y[1] (numeric) = 6.712501262200179 absolute error = 4.667377595524158e-12 relative error = 6.953261404663142e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.900032000004614 y[1] (closed_form) = 6.713488192189401 y[1] (numeric) = 6.713488192184729 absolute error = 4.671818487622659e-12 relative error = 6.958854106659398e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( x ) + 1.0 ; Iterations = 78125 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %