##############ECHO OF PROBLEM################# ##############temp/mult_sin_linpostode.ode################# diff ( y , x , 1 ) = sin(x) * (0.2 * x + 0.3); ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=5.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.1 $glob_look_poles=true $glob_max_iter=10000000 $glob_max_minutes=3 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(0.2 * sin(x) - 0.2 * cos(x) * x - 0.3 * cos(x)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 desired_abs_gbl_error 1.0e-10 range 4.9 estimated_steps 4900000.000000001 step_error 2.040816326530612e-17 est_needed_step_err 2.040816326530612e-17 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.027239825665583e-183 estimated_step_error 2.027239825665583e-183 best_h 2.0e-06 opt_iter 2 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3604577760145903e-175 estimated_step_error 1.3604577760145903e-175 best_h 4.0e-06 opt_iter 3 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.129879713575361e-168 estimated_step_error 9.129879713575361e-168 best_h 8.0e-06 opt_iter 4 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.126961414815378e-160 estimated_step_error 6.126961414815378e-160 best_h 1.6e-05 opt_iter 5 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.111738034403559e-152 estimated_step_error 4.111738034403559e-152 best_h 3.2e-05 opt_iter 6 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.759345827696917e-144 estimated_step_error 2.759345827696917e-144 best_h 6.4e-05 opt_iter 7 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.8517725404784156e-136 estimated_step_error 1.8517725404784156e-136 best_h 0.000128 opt_iter 8 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2427127790539326e-128 estimated_step_error 1.2427127790539326e-128 best_h 0.000256 opt_iter 9 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.339828617559618e-121 estimated_step_error 8.339828617559618e-121 best_h 0.000512 opt_iter 10 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.596931116830983e-113 estimated_step_error 5.596931116830983e-113 best_h 0.001024 opt_iter 11 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.756260862716069e-105 estimated_step_error 3.756260862716069e-105 best_h 0.002048 opt_iter 12 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.521084601725387e-97 estimated_step_error 2.521084601725387e-97 best_h 0.004096 opt_iter 13 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6922747020726002e-89 estimated_step_error 1.6922747020726002e-89 best_h 0.008192 opt_iter 14 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1362078404729782e-81 estimated_step_error 1.1362078404729782e-81 best_h 0.016384 opt_iter 15 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.632229531320506e-74 estimated_step_error 7.632229531320506e-74 best_h 0.032768 opt_iter 16 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.131656481142865e-66 estimated_step_error 5.131656481142865e-66 best_h 0.065536 opt_iter 17 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.456885975503126e-58 estimated_step_error 3.456885975503126e-58 best_h 0.131072 opt_iter 18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.337440336049756e-50 estimated_step_error 2.337440336049756e-50 best_h 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (analytic) -0.29843464955960264 y[1] (numeric) -0.29843464955960264 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.14922299557075605 Order of pole (three term test) -1.5376368245217757 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2 y[1] (analytic) -0.29348877030700987 y[1] (numeric) -0.2934887703070099 absolute error 5.551115123125783e-17 relative error 1.8914233472438916e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.23649985347841324 Order of pole (three term test) -2.5893340351086422 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.30000000000000004 y[1] (analytic) -0.28481709475295025 y[1] (numeric) -0.28481709475295025 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3134803168261286 Order of pole (three term test) -4.089134482349078 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4 y[1] (analytic) -0.27211950925936623 y[1] (numeric) -0.27211950925936623 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.37683307677171335 Order of pole (three term test) -5.9719525085864 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5 y[1] (analytic) -0.2551479170353085 y[1] (numeric) -0.2551479170353085 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.42382223121677226 Order of pole (three term test) -8.156174996021152 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6 y[1] (analytic) -0.2337124635830578 y[1] (numeric) -0.2337124635830578 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.75024234465293 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.4524251125435013 Order of pole (three term test) -10.547257410628978 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7 y[1] (analytic) -0.20768702495763672 y[1] (numeric) -0.2076870249576367 absolute error 2.7755575615628914e-17 relative error 1.3364135588773733e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 17.74052680812379 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.46141815688150256 Order of pole (three term test) -13.04186825884352 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7999999999999999 y[1] (analytic) -0.17701386811979158 y[1] (numeric) -0.17701386811979153 absolute error 5.551115123125783e-17 relative error 3.135977526556928e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.299717809198798 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.4504273433343056 Order of pole (three term test) -15.532391798409181 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8999999999999999 y[1] (analytic) -0.1417074028444223 y[1] (numeric) -0.14170740284442226 absolute error 2.7755575615628914e-17 relative error 1.958653892351778e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.41994141675118674 Order of pole (three term test) -17.911586807049716 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9999999999999999 y[1] (analytic) -0.10185695597249056 y[1] (numeric) -0.10185695597249056 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3712878038862431 Order of pole (three term test) -20.077197216288848 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0999999999999999 y[1] (analytic) -0.05762851112901321 y[1] (numeric) -0.057628511129013175 absolute error 3.469446951953614e-17 relative error 6.020365412853626e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.30657275263723305 Order of pole (three term test) -21.93631774664027 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2 y[1] (analytic) -0.009265370223958486 y[1] (numeric) -0.009265370223958458 absolute error 2.7755575615628914e-17 relative error 2.995625101289344e-13% Correct digits 15 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.22858869692930356 Order of pole (three term test) -23.40933314228273 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3 y[1] (analytic) 0.0429122930536697 y[1] (numeric) 0.04291229305366965 absolute error 4.85722573273506e-17 relative error 1.1318961041443784e-13% Correct digits 15 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.14069312489503463 Order of pole (three term test) -24.433271729060774 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4000000000000001 y[1] (analytic) 0.09850900311555238 y[1] (numeric) 0.0985090031155523 absolute error 8.326672684688674e-17 relative error 8.452702211310955e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.04666427402297914 Order of pole (three term test) -24.964441256594245 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5000000000000002 y[1] (analytic) 0.15705667632018927 y[1] (numeric) 0.15705667632018916 absolute error 1.1102230246251565e-16 relative error 7.068932379300835e-14% Correct digits 16 h 0.1 NO INFO (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] 1.6000000000000003 y[1] (analytic) 0.21801842443510022 y[1] (numeric) 0.21801842443510008 absolute error 1.3877787807814457e-16 relative error 6.365419731737214e-14% Correct digits 16 h 0.1 NO INFO (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] 1.7000000000000004 y[1] (analytic) 0.2807934384396298 y[1] (numeric) 0.28079343843962956 absolute error 2.220446049250313e-16 relative error 7.907756184009642e-14% Correct digits 16 h 0.1 NO INFO (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] 1.8000000000000005 y[1] (analytic) 0.3447229086730768 y[1] (numeric) 0.34472290867307653 absolute error 2.7755575615628914e-16 relative error 8.051561099454325e-14% Correct digits 16 h 0.1 NO INFO (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] 1.9000000000000006 y[1] (analytic) 0.4090969230046656 y[1] (numeric) 0.40909692300466527 absolute error 3.3306690738754696e-16 relative error 8.141515828114612e-14% Correct digits 16 h 0.1 NO INFO (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] 2.0000000000000004 y[1] (analytic) 0.47316227094813634 y[1] (numeric) 0.47316227094813607 absolute error 2.7755575615628914e-16 relative error 5.865973962803814e-14% Correct digits 16 h 0.1 NO INFO (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] 2.1000000000000005 y[1] (analytic) 0.5361310686416725 y[1] (numeric) 0.5361310686416721 absolute error 3.3306690738754696e-16 relative error 6.212415710796177e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 16.724046837609 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2000000000000006 y[1] (analytic) 0.5971901075328743 y[1] (numeric) 0.5971901075328739 absolute error 3.3306690738754696e-16 relative error 5.577234170263147e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 16.178247908607897 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3000000000000007 y[1] (analytic) 0.6555108186080109 y[1] (numeric) 0.6555108186080105 absolute error 3.3306690738754696e-16 relative error 5.081028381725577e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.000757307755926 Order of pole (ratio test) Not computed 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] (analytic) 0.7102597342324022 y[1] (numeric) 0.7102597342324017 absolute error 4.440892098500626e-16 relative error 6.252490299622608e-14% Correct digits 16 h 0.1 NO INFO (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] (analytic) 0.7606093212583387 y[1] (numeric) 0.7606093212583382 absolute error 4.440892098500626e-16 relative error 5.838598048146047e-14% Correct digits 16 h 0.1 NO INFO (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] (analytic) 0.80574905212683 y[1] (numeric) 0.8057490521268296 absolute error 4.440892098500626e-16 relative error 5.51150769185342e-14% Correct digits 16 h 0.1 NO INFO (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] 2.700000000000001 y[1] (analytic) 0.8448965753410977 y[1] (numeric) 0.8448965753410973 absolute error 4.440892098500626e-16 relative error 5.256136938071704e-14% Correct digits 16 h 0.1 NO INFO (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] 2.800000000000001 y[1] (analytic) 0.8773088430062274 y[1] (numeric) 0.8773088430062269 absolute error 4.440892098500626e-16 relative error 5.061948404946265e-14% Correct digits 16 h 0.1 NO INFO (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] 2.9000000000000012 y[1] (analytic) 0.9022930511744365 y[1] (numeric) 0.9022930511744359 absolute error 5.551115123125783e-16 relative error 6.152230825562025e-14% Correct digits 16 h 0.1 NO INFO (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] 3.0000000000000013 y[1] (analytic) 0.9192172485523746 y[1] (numeric) 0.9192172485523741 absolute error 5.551115123125783e-16 relative error 6.038958833581433e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.03384536758867499 Order of pole (three term test) -0.9251025304126405 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.1000000000000014 y[1] (analytic) 0.9275204707380753 y[1] (numeric) 0.9275204707380749 absolute error 4.440892098500626e-16 relative error 4.787918152325826e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.12847977794871798 Order of pole (three term test) -1.366853706959068 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.2000000000000015 y[1] (analytic) 0.9267222605615519 y[1] (numeric) 0.9267222605615514 absolute error 5.551115123125783e-16 relative error 5.99005263967875e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2174269304402032 Order of pole (three term test) -2.3087085894126114 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.3000000000000016 y[1] (analytic) 0.9164314402838605 y[1] (numeric) 0.9164314402838599 absolute error 5.551115123125783e-16 relative error 6.057316324073681e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2968404492838255 Order of pole (three term test) -3.709847800625693 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.4000000000000017 y[1] (analytic) 0.896354008322505 y[1] (numeric) 0.8963540083225047 absolute error 3.3306690738754696e-16 relative error 3.715796485485349e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3632900515317848 Order of pole (three term test) -5.509589792108625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.5000000000000018 y[1] (analytic) 0.8663000417528718 y[1] (numeric) 0.8663000417528713 absolute error 4.440892098500626e-16 relative error 5.126274829116854e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.41391059891839627 Order of pole (three term test) -7.630069764008032 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.600000000000002 y[1] (analytic) 0.8261894960018586 y[1] (numeric) 0.8261894960018583 absolute error 3.3306690738754696e-16 relative error 4.0313621632729844e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 16.552635941797476 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.44652566651422776 Order of pole (three term test) -9.979666482130465 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.700000000000002 y[1] (analytic) 0.7760568047971248 y[1] (numeric) 0.7760568047971245 absolute error 3.3306690738754696e-16 relative error 4.291785154498022e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 17.28347962319594 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.4597402593356695 Order of pole (three term test) -12.457016917765417 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.800000000000002 y[1] (analytic) 0.7160541964407365 y[1] (numeric) 0.7160541964407363 absolute error 2.220446049250313e-16 relative error 3.100946911961972e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.901844769773938 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.4529988347642132 Order of pole (three term test) -14.955433863653191 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.900000000000002 y[1] (analytic) 0.6464536566993551 y[1] (numeric) 0.6464536566993548 absolute error 2.220446049250313e-16 relative error 3.4348108735085576e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4266064557043118 Order of pole (three term test) -17.367526876113438 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.000000000000002 y[1] (analytic) 0.567647483888386 y[1] (numeric) 0.5676474838883855 absolute error 5.551115123125783e-16 relative error 9.77915921532962e-14% Correct digits 16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.38171260629792975 Order of pole (three term test) -19.589822260919224 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.100000000000001 y[1] (analytic) 0.4801473979043777 y[1] (numeric) 0.48014739790437694 absolute error 7.771561172376096e-16 relative error 1.618578212918654e-13% Correct digits 15 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.32025885588716774 Order of pole (three term test) -21.527182863480412 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.200000000000001 y[1] (analytic) 0.3845821818456788 y[1] (numeric) 0.3845821818456776 absolute error 1.2212453270876722e-15 relative error 3.1755119834899706e-13% Correct digits 15 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24489307972651714 Order of pole (three term test) -23.096842093564273 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.300000000000001 y[1] (analytic) 0.28169385226287963 y[1] (numeric) 0.28169385226287796 absolute error 1.6653345369377348e-15 relative error 5.911859714224886e-13% Correct digits 15 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1588542776353061 Order of pole (three term test) -24.231887496267515 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.4 y[1] (analytic) 0.1723323717966317 y[1] (numeric) 0.17233237179662958 absolute error 2.1094237467877974e-15 relative error 1.2240438199719753e-12% Correct digits 14 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.06583313541412593 Order of pole (three term test) -24.88405569037689 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.5 y[1] (analytic) 0.05744893578391623 y[1] (numeric) 0.05744893578391376 absolute error 2.4702462297909733e-15 relative error 4.299899025253239e-12% Correct digits 14 h 0.1 NO INFO (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] 4.6 y[1] (analytic) -0.061912117865925965 y[1] (numeric) -0.061912117865928845 absolute error 2.8796409701214998e-15 relative error 4.6511750354874275e-12% Correct digits 14 h 0.1 NO INFO (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] 4.699999999999999 y[1] (analytic) -0.1846227088188348 y[1] (numeric) -0.18462270881883813 absolute error 3.3306690738754696e-15 relative error 1.8040408437207818e-12% Correct digits 14 h 0.1 NO INFO (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] 4.799999999999999 y[1] (analytic) -0.3094816409008695 y[1] (numeric) -0.30948164090087327 absolute error 3.774758283725532e-15 relative error 1.2197034605146839e-12% Correct digits 14 h 0.1 NO INFO (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] (analytic) -0.43522635538576127 y[1] (numeric) -0.4352263553857655 absolute error 4.218847493575595e-15 relative error 9.693455925563687e-13% Correct digits 15 h 0.1 NO INFO (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] 4.999999999999998 y[1] (analytic) -0.5605456960348196 y[1] (numeric) -0.5605456960348243 absolute error 4.6629367034256575e-15 relative error 8.318566597532144e-13% Correct digits 15 h 0.1 NO INFO (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) * (0.2 * x + 0.3); Iterations 50 Total Elapsed Time 0.0 Seconds Elapsed Time(since restart) 0.0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 104.08163265306118%