##############ECHO OF PROBLEM################# ##############temp/lin_exppostode.ode################# diff ( y , x , 1 ) = exp ( 0.1 * x + 0.2 ) ; ! // BEGIN FIRST INPUT BLOCK max_terms=30; Digits=32; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=1.0; x_end=10.0; 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(10.0 * exp(0.1 * x + 0.2)); } // 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 = 9 estimated_steps = 9000000 step_error = 1.111111111111111e-21 est_needed_step_err = 1.111111111111111e-21 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 = 13.49858807576003 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 13.49858807576003 desired_abs_gbl_error = 1.349858807576003e-15 range = 9 estimated_steps = 9000000 step_error = 1.499843119528893e-20 est_needed_step_err = 1.499843119528893e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.347104861344876e-208 estimated_step_error = 3.347104861344876e-208 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 = 13.49858807576003 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 13.49858807576003 desired_abs_gbl_error = 1.349858807576003e-15 range = 9 estimated_steps = 4500000 step_error = 2.121098481069731e-20 est_needed_step_err = 2.121098481069731e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.246204053496958e-200 estimated_step_error = 2.246204053496958e-200 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 = 13.49858807576003 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 13.49858807576003 desired_abs_gbl_error = 1.349858807576003e-15 range = 9 estimated_steps = 2250000 step_error = 2.999686239057785e-20 est_needed_step_err = 2.999686239057785e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.507402029006731e-192 estimated_step_error = 1.507402029006731e-192 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 = 13.49858807576003 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 13.49858807576003 desired_abs_gbl_error = 1.349858807576003e-15 range = 9 estimated_steps = 1125000 step_error = 4.242196962139462e-20 est_needed_step_err = 4.242196962139462e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.011600385072704e-184 estimated_step_error = 1.011600385072704e-184 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 = 13.49858807576003 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 13.49858807576003 desired_abs_gbl_error = 1.349858807576003e-15 range = 9 estimated_steps = 562500 step_error = 5.999372478115571e-20 est_needed_step_err = 5.999372478115571e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.788735366993033e-177 estimated_step_error = 6.788735366993033e-177 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 = 13.49858807576003 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 13.49858807576003 desired_abs_gbl_error = 1.349858807576003e-15 range = 9 estimated_steps = 281250 step_error = 8.484393924278923e-20 est_needed_step_err = 8.484393924278923e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.555843319743209e-169 estimated_step_error = 4.555843319743209e-169 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 = 13.49858807576003 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 13.49858807576003 desired_abs_gbl_error = 1.349858807576003e-15 range = 9 estimated_steps = 140625 step_error = 1.199874495623114e-19 est_needed_step_err = 1.199874495623114e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.057374878677335e-161 estimated_step_error = 3.057374878677335e-161 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 = 13.49858807576003 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 13.49858807576003 desired_abs_gbl_error = 1.349858807576003e-15 range = 9 estimated_steps = 70312.5 step_error = 1.696878784855785e-19 est_needed_step_err = 1.696878784855785e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.05176979247448e-153 estimated_step_error = 2.05176979247448e-153 Double H and LOOP opt_iter = 9 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 = 13.49858807576003 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 13.49858807576003 desired_abs_gbl_error = 1.349858807576003e-15 range = 9 estimated_steps = 35156.25 step_error = 2.399748991246228e-19 est_needed_step_err = 2.399748991246228e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.376919726005822e-145 estimated_step_error = 1.376919726005822e-145 Double H and LOOP opt_iter = 10 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 = 13.49858807576003 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 13.49858807576003 desired_abs_gbl_error = 1.349858807576003e-15 range = 9 estimated_steps = 17578.125 step_error = 3.393757569711569e-19 est_needed_step_err = 3.393757569711569e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.240356243759382e-138 estimated_step_error = 9.240356243759382e-138 Double H and LOOP opt_iter = 11 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 = 13.49858807576003 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 13.49858807576003 desired_abs_gbl_error = 1.349858807576003e-15 range = 9 estimated_steps = 8789.0625 step_error = 4.799497982492456e-19 est_needed_step_err = 4.799497982492456e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.201103984310229e-130 estimated_step_error = 6.201103984310229e-130 Double H and LOOP opt_iter = 12 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 = 13.49858807576003 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 13.49858807576003 desired_abs_gbl_error = 1.349858807576003e-15 range = 9 estimated_steps = 4394.53125 step_error = 6.787515139423139e-19 est_needed_step_err = 6.787515139423139e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.161498330776565e-122 estimated_step_error = 4.161498330776565e-122 Double H and LOOP opt_iter = 13 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 = 13.49858807576003 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 13.49858807576003 desired_abs_gbl_error = 1.349858807576003e-15 range = 9 estimated_steps = 2197.265625 step_error = 9.598995964984913e-19 est_needed_step_err = 9.598995964984913e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.792744846942401e-114 estimated_step_error = 2.792744846942401e-114 Double H and LOOP opt_iter = 14 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 = 13.49858807576003 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 13.49858807576003 desired_abs_gbl_error = 1.349858807576003e-15 range = 9 estimated_steps = 1098.6328125 step_error = 1.357503027884628e-18 est_needed_step_err = 1.357503027884628e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.874193557403069e-106 estimated_step_error = 1.874193557403069e-106 Double H and LOOP opt_iter = 15 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 = 13.49858807576003 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 13.49858807576003 desired_abs_gbl_error = 1.349858807576003e-15 range = 9 estimated_steps = 549.31640625 step_error = 1.919799192996983e-18 est_needed_step_err = 1.919799192996983e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.257769086615724e-98 estimated_step_error = 1.257769086615724e-98 Double H and LOOP opt_iter = 16 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 = 13.49858807576003 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 13.49858807576003 desired_abs_gbl_error = 1.349858807576003e-15 range = 9 estimated_steps = 274.658203125 step_error = 2.715006055769255e-18 est_needed_step_err = 2.715006055769255e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.441001570888194e-91 estimated_step_error = 8.441001570888194e-91 Double H and LOOP opt_iter = 17 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 = 13.49858807576003 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 13.49858807576003 desired_abs_gbl_error = 1.349858807576003e-15 range = 9 estimated_steps = 137.3291015625 step_error = 3.839598385993965e-18 est_needed_step_err = 3.839598385993965e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.665004043908942e-83 estimated_step_error = 5.665004043908942e-83 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL 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 START of Soultion TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 13.49858807576003 y[1] (numeric) = 13.49858807576003 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 13.63425114132178 y[1] (numeric) = 13.63425114132178 absolute error = 1.77635683940025e-15 relative error = 1.302863517026312e-14 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (closed_form) = 13.77127764335957 y[1] (numeric) = 13.77127764335957 absolute error = 1.77635683940025e-15 relative error = 1.289899808429757e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (closed_form) = 13.9096812846378 y[1] (numeric) = 13.90968128463781 absolute error = 3.552713678800501e-15 relative error = 2.554130181777929e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (closed_form) = 14.04947590563594 y[1] (numeric) = 14.04947590563594 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (closed_form) = 14.19067548593257 y[1] (numeric) = 14.19067548593257 absolute error = 1.77635683940025e-15 relative error = 1.251777507815734e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.600000000000001 y[1] (closed_form) = 14.3332941456034 y[1] (numeric) = 14.33329414560341 absolute error = 1.77635683940025e-15 relative error = 1.239322113503915e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.700000000000001 y[1] (closed_form) = 14.47734614663324 y[1] (numeric) = 14.47734614663325 absolute error = 1.77635683940025e-15 relative error = 1.226990652436219e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.800000000000001 y[1] (closed_form) = 14.62284589434225 y[1] (numeric) = 14.62284589434225 absolute error = 1.77635683940025e-15 relative error = 1.214781891456262e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y[1] (closed_form) = 14.76980793882643 y[1] (numeric) = 14.76980793882643 absolute error = 1.77635683940025e-15 relative error = 1.202694609677772e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.000000000000001 y[1] (closed_form) = 14.91824697641271 y[1] (numeric) = 14.91824697641271 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.100000000000001 y[1] (closed_form) = 15.06817785112854 y[1] (numeric) = 15.06817785112854 absolute error = 1.77635683940025e-15 relative error = 1.178879660799338e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.200000000000001 y[1] (closed_form) = 15.21961555618634 y[1] (numeric) = 15.21961555618634 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.300000000000001 y[1] (closed_form) = 15.37257523548282 y[1] (numeric) = 15.37257523548282 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.400000000000001 y[1] (closed_form) = 15.52707218511336 y[1] (numeric) = 15.52707218511336 absolute error = 1.77635683940025e-15 relative error = 1.144038501413898e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.500000000000001 y[1] (closed_form) = 15.68312185490169 y[1] (numeric) = 15.68312185490169 absolute error = 1.77635683940025e-15 relative error = 1.132655128127477e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.600000000000001 y[1] (closed_form) = 15.84073984994482 y[1] (numeric) = 15.84073984994482 absolute error = 1.77635683940025e-15 relative error = 1.121385021297751e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.700000000000002 y[1] (closed_form) = 15.99994193217361 y[1] (numeric) = 15.9999419321736 absolute error = 1.77635683940025e-15 relative error = 1.110227053904646e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.800000000000002 y[1] (closed_form) = 16.16074402192894 y[1] (numeric) = 16.16074402192893 absolute error = 3.552713678800501e-15 relative error = 2.198360220284246e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.900000000000002 y[1] (closed_form) = 16.32316219955379 y[1] (numeric) = 16.32316219955379 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.000000000000002 y[1] (closed_form) = 16.48721270700128 y[1] (numeric) = 16.48721270700128 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.100000000000002 y[1] (closed_form) = 16.65291194945886 y[1] (numeric) = 16.65291194945886 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.200000000000002 y[1] (closed_form) = 16.82027649698887 y[1] (numeric) = 16.82027649698886 absolute error = 3.552713678800501e-15 relative error = 2.112161283101678e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.300000000000002 y[1] (closed_form) = 16.98932308618551 y[1] (numeric) = 16.98932308618551 absolute error = 3.552713678800501e-15 relative error = 2.091144927186246e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.400000000000002 y[1] (closed_form) = 17.16006862184859 y[1] (numeric) = 17.16006862184858 absolute error = 7.105427357601002e-15 relative error = 4.140675375012318e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.500000000000002 y[1] (closed_form) = 17.33253017867396 y[1] (numeric) = 17.33253017867395 absolute error = 3.552713678800501e-15 relative error = 2.04973748332011e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.600000000000002 y[1] (closed_form) = 17.50672500296102 y[1] (numeric) = 17.50672500296101 absolute error = 3.552713678800501e-15 relative error = 2.029342254590513e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.700000000000002 y[1] (closed_form) = 17.68267051433736 y[1] (numeric) = 17.68267051433735 absolute error = 3.552713678800501e-15 relative error = 2.009149961777499e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.800000000000002 y[1] (closed_form) = 17.86038430750074 y[1] (numeric) = 17.86038430750073 absolute error = 3.552713678800501e-15 relative error = 1.989158585634961e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.900000000000003 y[1] (closed_form) = 18.03988415397858 y[1] (numeric) = 18.03988415397857 absolute error = 7.105427357601002e-15 relative error = 3.938732254017245e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.000000000000003 y[1] (closed_form) = 18.22118800390509 y[1] (numeric) = 18.22118800390509 absolute error = 3.552713678800501e-15 relative error = 1.94977060663613e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.100000000000002 y[1] (closed_form) = 18.40431398781638 y[1] (numeric) = 18.40431398781638 absolute error = 3.552713678800501e-15 relative error = 1.930370064949115e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.200000000000002 y[1] (closed_form) = 18.58928041846342 y[1] (numeric) = 18.58928041846342 absolute error = 3.552713678800501e-15 relative error = 1.911162561877242e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.300000000000002 y[1] (closed_form) = 18.77610579264343 y[1] (numeric) = 18.77610579264343 absolute error = 3.552713678800501e-15 relative error = 1.892146176654198e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.400000000000001 y[1] (closed_form) = 18.96480879304952 y[1] (numeric) = 18.96480879304951 absolute error = 3.552713678800501e-15 relative error = 1.873319007625612e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.500000000000001 y[1] (closed_form) = 19.15540829013896 y[1] (numeric) = 19.15540829013896 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.600000000000001 y[1] (closed_form) = 19.34792334402032 y[1] (numeric) = 19.34792334402032 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (closed_form) = 19.5423732063594 y[1] (numeric) = 19.5423732063594 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (closed_form) = 19.73877732230448 y[1] (numeric) = 19.73877732230448 absolute error = 3.552713678800501e-15 relative error = 1.799865118689999e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.899999999999999 y[1] (closed_form) = 19.93715533243082 y[1] (numeric) = 19.93715533243083 absolute error = 3.552713678800501e-15 relative error = 1.78195616152996e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.999999999999999 y[1] (closed_form) = 20.13752707470477 y[1] (numeric) = 20.13752707470477 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 5.099999999999999 y[1] (closed_form) = 20.33991258646751 y[1] (numeric) = 20.33991258646751 absolute error = 3.552713678800501e-15 relative error = 1.746671065422465e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 5.199999999999998 y[1] (closed_form) = 20.54433210643888 y[1] (numeric) = 20.54433210643888 absolute error = 3.552713678800501e-15 relative error = 1.729291397935994e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 5.299999999999998 y[1] (closed_form) = 20.75080607674122 y[1] (numeric) = 20.75080607674123 absolute error = 7.105427357601002e-15 relative error = 3.424169322060796e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 5.399999999999998 y[1] (closed_form) = 20.95935514494364 y[1] (numeric) = 20.95935514494365 absolute error = 7.105427357601002e-15 relative error = 3.390098268035292e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 5.499999999999997 y[1] (closed_form) = 21.17000016612674 y[1] (numeric) = 21.17000016612675 absolute error = 3.552713678800501e-15 relative error = 1.678183113330842e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 5.599999999999997 y[1] (closed_form) = 21.38276220496818 y[1] (numeric) = 21.38276220496819 absolute error = 7.105427357601002e-15 relative error = 3.322969824707722e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 5.699999999999997 y[1] (closed_form) = 21.59766253784915 y[1] (numeric) = 21.59766253784915 absolute error = 7.105427357601002e-15 relative error = 3.289905722505382e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 5.799999999999996 y[1] (closed_form) = 21.814722654982 y[1] (numeric) = 21.81472265498201 absolute error = 1.06581410364015e-14 relative error = 4.885755920425336e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 5.899999999999996 y[1] (closed_form) = 22.03396426255935 y[1] (numeric) = 22.03396426255937 absolute error = 1.4210854715202e-14 relative error = 6.449522449008158e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 5.999999999999996 y[1] (closed_form) = 22.25540928492467 y[1] (numeric) = 22.25540928492468 absolute error = 1.06581410364015e-14 relative error = 4.78901147130154e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 6.099999999999995 y[1] (closed_form) = 22.4790798667647 y[1] (numeric) = 22.47907986676472 absolute error = 1.4210854715202e-14 relative error = 6.321813347979931e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 6.199999999999995 y[1] (closed_form) = 22.70499837532405 y[1] (numeric) = 22.70499837532406 absolute error = 1.06581410364015e-14 relative error = 4.694182690620602e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 6.299999999999994 y[1] (closed_form) = 22.93318740264182 y[1] (numeric) = 22.93318740264183 absolute error = 1.4210854715202e-14 relative error = 6.196633056582866e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 6.399999999999994 y[1] (closed_form) = 23.1636697678109 y[1] (numeric) = 23.16366976781092 absolute error = 1.77635683940025e-14 relative error = 7.668719409343083e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 6.499999999999994 y[1] (closed_form) = 23.39646851925989 y[1] (numeric) = 23.39646851925991 absolute error = 1.77635683940025e-14 relative error = 7.592414376289138e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 6.599999999999993 y[1] (closed_form) = 23.63160693705793 y[1] (numeric) = 23.63160693705795 absolute error = 1.77635683940025e-14 relative error = 7.516868590999854e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 6.699999999999993 y[1] (closed_form) = 23.86910853524276 y[1] (numeric) = 23.86910853524277 absolute error = 1.4210854715202e-14 relative error = 5.953659599066998e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 6.799999999999993 y[1] (closed_form) = 24.10899706417208 y[1] (numeric) = 24.1089970641721 absolute error = 2.131628207280301e-14 relative error = 8.841629544383132e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 6.899999999999992 y[1] (closed_form) = 24.35129651289873 y[1] (numeric) = 24.35129651289875 absolute error = 2.131628207280301e-14 relative error = 8.753653860488252e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 6.999999999999992 y[1] (closed_form) = 24.59603111156948 y[1] (numeric) = 24.5960311115695 absolute error = 2.131628207280301e-14 relative error = 8.666553549274158e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 7.099999999999992 y[1] (closed_form) = 24.84322533384815 y[1] (numeric) = 24.84322533384817 absolute error = 2.131628207280301e-14 relative error = 8.580319900637142e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 7.199999999999991 y[1] (closed_form) = 25.09290389936296 y[1] (numeric) = 25.09290389936298 absolute error = 1.77635683940025e-14 relative error = 7.079120242617066e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 7.299999999999991 y[1] (closed_form) = 25.34509177617852 y[1] (numeric) = 25.34509177617855 absolute error = 2.131628207280301e-14 relative error = 8.410418183152077e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 7.399999999999991 y[1] (closed_form) = 25.59981418329269 y[1] (numeric) = 25.59981418329271 absolute error = 2.486899575160351e-14 relative error = 9.714521977989145e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 7.49999999999999 y[1] (closed_form) = 25.85709659315844 y[1] (numeric) = 25.85709659315846 absolute error = 2.486899575160351e-14 relative error = 9.617860869260792e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 7.59999999999999 y[1] (closed_form) = 26.11696473423115 y[1] (numeric) = 26.11696473423118 absolute error = 2.486899575160351e-14 relative error = 9.522161554634275e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 7.69999999999999 y[1] (closed_form) = 26.3794445935415 y[1] (numeric) = 26.37944459354152 absolute error = 2.131628207280301e-14 relative error = 8.080640969227186e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 7.799999999999989 y[1] (closed_form) = 26.64456241929414 y[1] (numeric) = 26.64456241929417 absolute error = 2.842170943040401e-14 relative error = 1.066698299756012e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 7.899999999999989 y[1] (closed_form) = 26.91234472349259 y[1] (numeric) = 26.91234472349262 absolute error = 2.842170943040401e-14 relative error = 1.05608447433396e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 7.999999999999988 y[1] (closed_form) = 27.18281828459043 y[1] (numeric) = 27.18281828459045 absolute error = 2.842170943040401e-14 relative error = 1.045576258239415e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 8.099999999999989 y[1] (closed_form) = 27.45601015016913 y[1] (numeric) = 27.45601015016917 absolute error = 3.197442310920451e-14 relative error = 1.164569175722261e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 8.199999999999989 y[1] (closed_form) = 27.73194763964295 y[1] (numeric) = 27.73194763964298 absolute error = 3.197442310920451e-14 relative error = 1.15298151881323e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 8.299999999999988 y[1] (closed_form) = 28.01065834699076 y[1] (numeric) = 28.01065834699079 absolute error = 3.552713678800501e-14 relative error = 1.268343512241002e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 8.399999999999988 y[1] (closed_form) = 28.29217014351556 y[1] (numeric) = 28.2921701435156 absolute error = 3.552713678800501e-14 relative error = 1.25572328343104e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 8.499999999999988 y[1] (closed_form) = 28.5765111806316 y[1] (numeric) = 28.57651118063164 absolute error = 3.907985046680551e-14 relative error = 1.367551490795447e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 8.599999999999987 y[1] (closed_form) = 28.86370989267954 y[1] (numeric) = 28.86370989267959 absolute error = 4.263256414560601e-14 relative error = 1.47702995575141e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 8.699999999999987 y[1] (closed_form) = 29.15379499976993 y[1] (numeric) = 29.15379499976997 absolute error = 4.263256414560601e-14 relative error = 1.462333262134225e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 8.799999999999986 y[1] (closed_form) = 29.4467955106552 y[1] (numeric) = 29.44679551065524 absolute error = 4.263256414560601e-14 relative error = 1.447782803061868e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 8.899999999999986 y[1] (closed_form) = 29.74274072563062 y[1] (numeric) = 29.74274072563066 absolute error = 3.907985046680551e-14 relative error = 1.313929029853281e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 8.999999999999986 y[1] (closed_form) = 30.04166023946429 y[1] (numeric) = 30.04166023946433 absolute error = 4.973799150320701e-14 relative error = 1.655633913263842e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 9.099999999999985 y[1] (closed_form) = 30.34358394435671 y[1] (numeric) = 30.34358394435676 absolute error = 4.618527782440651e-14 relative error = 1.52207721767804e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 9.199999999999985 y[1] (closed_form) = 30.64854203292997 y[1] (numeric) = 30.64854203293002 absolute error = 4.973799150320701e-14 relative error = 1.622850165262889e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 9.299999999999985 y[1] (closed_form) = 30.95656500124707 y[1] (numeric) = 30.95656500124712 absolute error = 4.618527782440651e-14 relative error = 1.491938069438452e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 9.399999999999984 y[1] (closed_form) = 31.26768365186151 y[1] (numeric) = 31.26768365186156 absolute error = 4.618527782440651e-14 relative error = 1.477093037611594e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 9.499999999999984 y[1] (closed_form) = 31.58192909689762 y[1] (numeric) = 31.58192909689768 absolute error = 5.329070518200751e-14 relative error = 1.687379672676246e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 9.599999999999984 y[1] (closed_form) = 31.89933276116179 y[1] (numeric) = 31.89933276116185 absolute error = 5.329070518200751e-14 relative error = 1.670589964404843e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 9.699999999999983 y[1] (closed_form) = 32.21992638528495 y[1] (numeric) = 32.219926385285 absolute error = 4.973799150320701e-14 relative error = 1.543702828753907e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 9.799999999999983 y[1] (closed_form) = 32.54374202889665 y[1] (numeric) = 32.54374202889671 absolute error = 5.684341886080801e-14 relative error = 1.746677404532487e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 9.899999999999983 y[1] (closed_form) = 32.87081207383113 y[1] (numeric) = 32.87081207383118 absolute error = 4.973799150320701e-14 relative error = 1.513135464724465e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 9.999999999999982 y[1] (closed_form) = 33.20116922736541 y[1] (numeric) = 33.20116922736548 absolute error = 6.394884621840902e-14 relative error = 1.926102233944835e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 Finished! diff ( y , x , 1 ) = exp ( 0.1 * x + 0.2 ) ; Iterations = 91 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 102.2 %