##############ECHO OF PROBLEM################# ##############temp/div_c_exppostode.ode################# diff ( y , x , 1 ) = 2.0 / exp ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(1.0); x_end=c(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=8; glob_max_minutes=(20.0); glob_subiter_method=3; glob_max_iter=1000; glob_upper_ratio_limit=c(1.11); glob_lower_ratio_limit=c(0.99); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(-2.0)/exp(c(x))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = -0.7357588823428847 y[1] (numeric) = -0.7357588823428847 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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) = -0.665742167396159 y[1] (numeric) = -0.6657421673961592 absolute error = 2.220446049250313e-16 relative error = 3.33529428958194e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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) = -0.6023884238244041 y[1] (numeric) = -0.6023884238244043 absolute error = 2.220446049250313e-16 relative error = 3.686070252069738e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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) = -0.5450635860680251 y[1] (numeric) = -0.5450635860680253 absolute error = 2.220446049250313e-16 relative error = 4.073737644571246e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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) = -0.4931939278832128 y[1] (numeric) = -0.4931939278832131 absolute error = 3.33066907387547e-16 relative error = 6.753264558975196e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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) = -0.4462603202968594 y[1] (numeric) = -0.4462603202968598 absolute error = 3.885780586188048e-16 relative error = 8.707430191425411e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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) = -0.4037930359893106 y[1] (numeric) = -0.4037930359893109 absolute error = 3.33066907387547e-16 relative error = 8.248455958917629e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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) = -0.365367048105469 y[1] (numeric) = -0.3653670481054694 absolute error = 3.885780586188048e-16 relative error = 1.063527925229413e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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) = -0.3305977764431728 y[1] (numeric) = -0.3305977764431732 absolute error = 3.885780586188048e-16 relative error = 1.17538013352488e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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) = -0.2991372384452698 y[1] (numeric) = -0.2991372384452703 absolute error = 4.440892098500626e-16 relative error = 1.484566790006364e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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) = -0.2706705664732251 y[1] (numeric) = -0.2706705664732256 absolute error = 4.440892098500626e-16 relative error = 1.640700042255951e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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) = -0.2449128565059637 y[1] (numeric) = -0.244912856505964 absolute error = 3.608224830031759e-16 relative error = 1.473268852239245e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 2.2 y[1] (closed_form) = -0.2216063167246677 y[1] (numeric) = -0.221606316724668 absolute error = 2.498001805406602e-16 relative error = 1.12722500077027e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 2.3 y[1] (closed_form) = -0.2005176874456075 y[1] (numeric) = -0.2005176874456077 absolute error = 1.665334536937735e-16 relative error = 8.305175259860674e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 2.399999999999999 y[1] (closed_form) = -0.1814359065788251 y[1] (numeric) = -0.1814359065788252 absolute error = 1.110223024625157e-16 relative error = 6.119092111146249e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 2.499999999999999 y[1] (closed_form) = -0.1641699972477977 y[1] (numeric) = -0.1641699972477978 absolute error = 5.551115123125783e-17 relative error = 3.381321323132475e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 2.599999999999999 y[1] (closed_form) = -0.1485471564286679 y[1] (numeric) = -0.1485471564286679 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 2.699999999999998 y[1] (closed_form) = -0.1344110254794997 y[1] (numeric) = -0.1344110254794997 absolute error = 2.775557561562891e-17 relative error = 2.064977595149899e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 2.799999999999998 y[1] (closed_form) = -0.1216201252504362 y[1] (numeric) = -0.1216201252504361 absolute error = 9.71445146547012e-17 relative error = 7.987536146231094e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 2.899999999999998 y[1] (closed_form) = -0.1100464401128147 y[1] (numeric) = -0.1100464401128146 absolute error = 1.387778780781446e-16 relative error = 1.261084665127519e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 2.999999999999997 y[1] (closed_form) = -0.09957413673572815 y[1] (numeric) = -0.09957413673572799 absolute error = 1.665334536937735e-16 relative error = 1.672456916556121e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 3.099999999999997 y[1] (closed_form) = -0.09009840478711589 y[1] (numeric) = -0.09009840478711569 absolute error = 2.081668171172169e-16 relative error = 2.310438432390368e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 3.199999999999997 y[1] (closed_form) = -0.0815244079567327 y[1] (numeric) = -0.08152440795673248 absolute error = 2.220446049250313e-16 relative error = 2.723657987714264e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 3.299999999999996 y[1] (closed_form) = -0.07376633480248028 y[1] (numeric) = -0.07376633480248004 absolute error = 2.359223927328458e-16 relative error = 3.198239323731633e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 3.399999999999996 y[1] (closed_form) = -0.06674653992065244 y[1] (numeric) = -0.06674653992065217 absolute error = 2.636779683484747e-16 relative error = 3.950436511944023e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 3.499999999999996 y[1] (closed_form) = -0.06039476684463727 y[1] (numeric) = -0.06039476684463699 absolute error = 2.706168622523819e-16 relative error = 4.480799850565384e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 3.599999999999995 y[1] (closed_form) = -0.05464744489458539 y[1] (numeric) = -0.05464744489458509 absolute error = 2.983724378680108e-16 relative error = 5.459952216312575e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 3.699999999999995 y[1] (closed_form) = -0.04944705294067904 y[1] (numeric) = -0.04944705294067872 absolute error = 3.191891195797325e-16 relative error = 6.455169734031659e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 3.799999999999994 y[1] (closed_form) = -0.04474154371233143 y[1] (numeric) = -0.04474154371233111 absolute error = 3.261280134836397e-16 relative error = 7.2891542495829e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 3.899999999999994 y[1] (closed_form) = -0.04048382289160902 y[1] (numeric) = -0.04048382289160866 absolute error = 3.538835890992686e-16 relative error = 8.741357999879434e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 3.999999999999994 y[1] (closed_form) = -0.03663127777746859 y[1] (numeric) = -0.03663127777746823 absolute error = 3.608224830031759e-16 relative error = 9.850120031169456e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 4.099999999999993 y[1] (closed_form) = -0.03314535080352271 y[1] (numeric) = -0.03314535080352234 absolute error = 3.747002708109903e-16 relative error = 1.130476105177221e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 4.199999999999993 y[1] (closed_form) = -0.02999115364095562 y[1] (numeric) = -0.02999115364095523 absolute error = 3.851086116668512e-16 relative error = 1.284074018216327e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 4.299999999999993 y[1] (closed_form) = -0.02713711802440206 y[1] (numeric) = -0.02713711802440166 absolute error = 3.989863994746656e-16 relative error = 1.470260766511358e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 4.399999999999992 y[1] (closed_form) = -0.02455467980613707 y[1] (numeric) = -0.02455467980613666 absolute error = 4.093947403305265e-16 relative error = 1.667277861339509e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 4.499999999999992 y[1] (closed_form) = -0.02221799307648479 y[1] (numeric) = -0.02221799307648437 absolute error = 4.163336342344337e-16 relative error = 1.873857970885207e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 4.599999999999992 y[1] (closed_form) = -0.02010367148926733 y[1] (numeric) = -0.02010367148926691 absolute error = 4.232725281383409e-16 relative error = 2.105448889593683e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 4.699999999999991 y[1] (closed_form) = -0.01819055420339179 y[1] (numeric) = -0.01819055420339136 absolute error = 4.267419750902945e-16 relative error = 2.3459536763906e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 4.799999999999991 y[1] (closed_form) = -0.01645949409804021 y[1] (numeric) = -0.01645949409803977 absolute error = 4.336808689942018e-16 relative error = 2.634837173068637e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 4.899999999999991 y[1] (closed_form) = -0.01489316614184882 y[1] (numeric) = -0.01489316614184838 absolute error = 4.423544863740858e-16 relative error = 2.970184325890911e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 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] = 4.99999999999999 y[1] (closed_form) = -0.01347589399817107 y[1] (numeric) = -0.01347589399817062 absolute error = 4.475586568020162e-16 relative error = 3.321179706984623e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = 2.0 / exp ( x ) ; Iterations = 81 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 102.5 %