##############ECHO OF PROBLEM################# ##############temp/lin_arctanpostode.ode################# diff ( y , x , 1 ) = arctan ( 0.1 * x + 0.2 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-1.0 x_end=-0.6 ## ## Trouble further ## $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=100 $glob_max_h=0.00001 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.01 $glob_look_poles=true $glob_max_iter=1000000000 $glob_max_minutes=30.0 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(10.0 * (0.1 * x + 0.2) * arctan(0.1 * x + 0.2) - 5.0 * ln(1.0 + expt((0.1 * x + 0.2) , 2))) 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 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-10 range 0.4 estimated_steps 400000.00000000006 step_error 2.4999999999999997e-16 est_needed_step_err 2.4999999999999997e-16 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.4711623349351338e-185 estimated_step_error 2.4711623349351338e-185 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 1.658368769248977e-177 estimated_step_error 1.658368769248977e-177 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 1.1129121717641285e-169 estimated_step_error 1.1129121717641285e-169 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 7.468623531193766e-162 estimated_step_error 7.468623531193766e-162 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 5.0121035405559584e-154 estimated_step_error 5.0121035405559584e-154 best_h 1.0e-05 START of Soultion TOP MAIN SOLVE Loop x[1] -1.0 y[1] (analytic) 0.04991699822532158 y[1] (numeric) 0.04991699822532158 absolute error 0.0 relative error 0.0% Correct digits 16 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.166893977859186 Order of pole (six term test) -0.49449227018263464 TOP MAIN SOLVE Loop x[1] -0.9899900000000456 y[1] (analytic) 0.050919641509209135 y[1] (numeric) 0.05091964150921465 absolute error 5.5164206536062466e-15 relative error 1.0833581089938678e-11% Correct digits 13 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.17011965822674 Order of pole (six term test) -0.49455465018363043 TOP MAIN SOLVE Loop x[1] -0.9799900000000911 y[1] (analytic) 0.051931187118171164 y[1] (numeric) 0.05193118711818169 absolute error 1.0526302052227265e-14 relative error 2.026971197148702e-11% Correct digits 13 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.173364485546754 Order of pole (six term test) -0.4946307396501375 TOP MAIN SOLVE Loop x[1] -0.9699900000001366 y[1] (analytic) 0.05295262975485577 y[1] (numeric) 0.05295262975487172 absolute error 1.5952517085082718e-14 relative error 3.0126014815382926e-11% Correct digits 13 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.176631102759696 Order of pole (six term test) -0.49472137462771215 TOP MAIN SOLVE Loop x[1] -0.9599900000001821 y[1] (analytic) 0.05398396741165431 y[1] (numeric) 0.05398396741167503 absolute error 2.0719537197066984e-14 relative error 3.8380908611385154e-11% Correct digits 13 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.179918925611203 Order of pole (six term test) -0.4948273564655583 TOP MAIN SOLVE Loop x[1] -0.9499900000002276 y[1] (analytic) 0.05502519806219495 y[1] (numeric) 0.055025198062222065 absolute error 2.711719737646945e-14 relative error 4.928141711697048e-11% Correct digits 13 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.18322735395604 Order of pole (six term test) -0.4949495070250851 TOP MAIN SOLVE Loop x[1] -0.9399900000002731 y[1] (analytic) 0.05607631966137489 y[1] (numeric) 0.056076319661406554 absolute error 3.166217288352868e-14 relative error 5.646264425826333e-11% Correct digits 13 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.186555772006898 Order of pole (six term test) -0.49508866813496333 TOP MAIN SOLVE Loop x[1] -0.9299900000003186 y[1] (analytic) 0.05713733014537212 y[1] (numeric) 0.057137330145409775 absolute error 3.765737721650453e-14 relative error 6.590678479497457e-11% Correct digits 13 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.189903548621675 Order of pole (six term test) -0.495245700982462 TOP MAIN SOLVE Loop x[1] -0.9199900000003641 y[1] (analytic) 0.058208227431681324 y[1] (numeric) 0.0582082274317244 absolute error 4.3076653355456074e-14 relative error 7.400440668978437e-11% Correct digits 13 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.193270037629937 Order of pole (six term test) -0.49542148544009024 TOP MAIN SOLVE Loop x[1] -0.9099900000004096 y[1] (analytic) 0.05928900941912939 y[1] (numeric) 0.059289009419178314 absolute error 4.892614091644987e-14 relative error 8.252143423510129e-11% Correct digits 13 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.196654578198526 Order of pole (six term test) -0.4956169193276896 TOP MAIN SOLVE Loop x[1] -0.8999900000004551 y[1] (analytic) 0.060379673987904114 y[1] (numeric) 0.06037967398795923 absolute error 5.5115634278735115e-14 relative error 9.128176857956612e-11% Correct digits 13 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.200056495236412 Order of pole (six term test) -0.4958329176100733 TOP MAIN SOLVE Loop x[1] -0.8899900000005007 y[1] (analytic) 0.06148021899957869 y[1] (numeric) 0.061480218999639374 absolute error 6.068756608357262e-14 relative error 9.871071878255427e-11% Correct digits 13 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.203475099839558 Order of pole (six term test) -0.49607041152900777 TOP MAIN SOLVE Loop x[1] -0.8799900000005462 y[1] (analytic) 0.06259064229713324 y[1] (numeric) 0.06259064229719993 absolute error 6.669664820435628e-14 relative error 1.0656009549755188e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.206909689774783 Order of pole (six term test) -0.4963303476714902 TOP MAIN SOLVE Loop x[1] -0.8699900000005917 y[1] (analytic) 0.06371094170498418 y[1] (numeric) 0.06371094170505612 absolute error 7.194245199571014e-14 relative error 1.1292008887396811e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.210359550002693 Order of pole (six term test) -0.4966136869741504 TOP MAIN SOLVE Loop x[1] -0.8599900000006372 y[1] (analytic) 0.0648411150290049 y[1] (numeric) 0.06484111502908245 absolute error 7.754907827006718e-14 relative error 1.1959861923314816e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.213823953240066 Order of pole (six term test) -0.4969214036636149 TOP MAIN SOLVE Loop x[1] -0.8499900000006827 y[1] (analytic) 0.06598116005655447 y[1] (numeric) 0.06598116005663823 absolute error 8.376632720796806e-14 relative error 1.2695491733726625e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.217302160559916 Order of pole (six term test) -0.497254484135663 TOP MAIN SOLVE Loop x[1] -0.8399900000007282 y[1] (analytic) 0.0671310745565032 y[1] (numeric) 0.06713107455659233 absolute error 8.912315330178444e-14 relative error 1.3275990871674612e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.220793422029844 Order of pole (six term test) -0.4976139257724501 TOP MAIN SOLVE Loop x[1] -0.8299900000007737 y[1] (analytic) 0.06829085627925394 y[1] (numeric) 0.06829085627935001 absolute error 9.607592499349948e-14 relative error 1.406863674407995e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.224296977387109 Order of pole (six term test) -0.4980007357006677 TOP MAIN SOLVE Loop x[1] -0.8199900000008192 y[1] (analytic) 0.06946050295677675 y[1] (numeric) 0.0694605029568781 absolute error 1.0134948436046898e-13 relative error 1.459095169862732e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.227812056750032 Order of pole (six term test) -0.49841592949120006 TOP MAIN SOLVE Loop x[1] -0.8099900000008647 y[1] (analytic) 0.07064001230262319 y[1] (numeric) 0.07064001230273124 absolute error 1.0805245587164336e-13 relative error 1.5296211360884896e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.231337881364208 Order of pole (six term test) -0.49886052980319917 TOP MAIN SOLVE Loop x[1] -0.7999900000009103 y[1] (analytic) 0.07182938201196445 y[1] (numeric) 0.07182938201207834 absolute error 1.1388112675092543e-13 relative error 1.5854393224760935e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.234873664382956 Order of pole (six term test) -0.4993355649735989 TOP MAIN SOLVE Loop x[1] -0.7899900000009558 y[1] (analytic) 0.07302860976160921 y[1] (numeric) 0.07302860976172942 absolute error 1.2020939799128882e-13 relative error 1.6460589676250734e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.238418611679968 Order of pole (six term test) -0.49984206755565097 TOP MAIN SOLVE Loop x[1] -0.7799900000010013 y[1] (analytic) 0.07423769321003587 y[1] (numeric) 0.07423769321016178 absolute error 1.2591316878030057e-13 relative error 1.6960813750511164e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.241971922693166 Order of pole (six term test) -0.5003810728081639 TOP MAIN SOLVE Loop x[1] -0.7699900000010468 y[1] (analytic) 0.07545662999741495 y[1] (numeric) 0.07545662999754703 absolute error 1.3207490656697018e-13 relative error 1.7503419722229166e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.245532791297872 Order of pole (six term test) -0.5009536171389417 TOP MAIN SOLVE Loop x[1] -0.7599900000010923 y[1] (analytic) 0.07668541774563967 y[1] (numeric) 0.07668541774577838 absolute error 1.387084891391055e-13 relative error 1.808798767963841e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.249100406707711 Order of pole (six term test) -0.5015607365050894 TOP MAIN SOLVE Loop x[1] -0.7499900000011378 y[1] (analytic) 0.07792405405835298 y[1] (numeric) 0.07792405405849784 absolute error 1.448563491379673e-13 relative error 1.85894267037868e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.252673954400978 Order of pole (six term test) -0.5022034647740359 TOP MAIN SOLVE Loop x[1] -0.7399900000011833 y[1] (analytic) 0.07917253652097198 y[1] (numeric) 0.07917253652112338 absolute error 1.5140666498325572e-13 relative error 1.912363448695997e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.25625261707061 Order of pole (six term test) -0.5028828320486465 TOP MAIN SOLVE Loop x[1] -0.7299900000012288 y[1] (analytic) 0.08043086270071868 y[1] (numeric) 0.08043086270087713 absolute error 1.5844270340181765e-13 relative error 1.9699242067237196e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.259835575595384 Order of pole (six term test) -0.503599862960419 TOP MAIN SOLVE Loop x[1] -0.7199900000012743 y[1] (analytic) 0.08169903014664687 y[1] (numeric) 0.08169903014681276 absolute error 1.6589507545461402e-13 relative error 2.0305635838863476e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.263422010030315 Order of pole (six term test) -0.5043555749342996 TOP MAIN SOLVE Loop x[1] -0.7099900000013198 y[1] (analytic) 0.0829770363896713 y[1] (numeric) 0.08297703638984374 absolute error 1.7244539129990244e-13 relative error 2.0782303008518615e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.267011100612834 Order of pole (six term test) -0.5051509764307678 TOP MAIN SOLVE Loop x[1] -0.6999900000013654 y[1] (analytic) 0.08426487894259359 y[1] (numeric) 0.08426487894277186 absolute error 1.782740621791845e-13 relative error 2.115638975766354e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.270602028783367 Order of pole (six term test) -0.505987065167929 TOP MAIN SOLVE Loop x[1] -0.6899900000014109 y[1] (analytic) 0.08556255530012949 y[1] (numeric) 0.08556255530031515 absolute error 1.856570452929418e-13 relative error 2.1698398866385986e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.274193978216056 Order of pole (six term test) -0.5068648263303128 TOP MAIN SOLVE Loop x[1] -0.6799900000014564 y[1] (analytic) 0.08687006293894421 y[1] (numeric) 0.08687006293913645 absolute error 1.9223511671384585e-13 relative error 2.2129040800736666e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.277786135858006 Order of pole (six term test) -0.5077852307676203 TOP MAIN SOLVE Loop x[1] -0.6699900000015019 y[1] (analytic) 0.08818739931767458 y[1] (numeric) 0.08818739931787298 absolute error 1.9839685450051547e-13 relative error 2.249718849127606e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.281377692973184 Order of pole (six term test) -0.5087492331895831 TOP MAIN SOLVE Loop x[1] -0.6599900000015474 y[1] (analytic) 0.08951456187695797 y[1] (numeric) 0.08951456187716386 absolute error 2.0589085991673528e-13 relative error 2.3000823061586568e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.28496784618806 Order of pole (six term test) -0.5097577703619862 TOP MAIN SOLVE Loop x[1] -0.6499900000015929 y[1] (analytic) 0.09085154803946803 y[1] (numeric) 0.09085154803968085 absolute error 2.128158760328347e-13 relative error 2.3424573452549484e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.288555798535544 Order of pole (six term test) -0.510811759309604 TOP MAIN SOLVE Loop x[1] -0.6399900000016384 y[1] (analytic) 0.09219835520993729 y[1] (numeric) 0.0921983552101566 absolute error 2.1931068072689186e-13 relative error 2.3786832230088873e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.29214076049435 Order of pole (six term test) -0.5119120955308407 TOP MAIN SOLVE Loop x[1] -0.6299900000016839 y[1] (analytic) 0.09355498077518698 y[1] (numeric) 0.09355498077541399 absolute error 2.2701285296022888e-13 relative error 2.426518086789433e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.295721951019583 Order of pole (six term test) -0.5130596512310337 TOP MAIN SOLVE Loop x[1] -0.6199900000017294 y[1] (analytic) 0.094921422104163 y[1] (numeric) 0.09492142210439701 absolute error 2.3400725801536737e-13 relative error 2.465273410659367e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.299298598561508 Order of pole (six term test) -0.5142552735795665 TOP MAIN SOLVE Loop x[1] -0.609990000001775 y[1] (analytic) 0.09629767654795937 y[1] (numeric) 0.0962976765481998 absolute error 2.4043267377038546e-13 relative error 2.4967650559112105e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.30286994206889 Order of pole (six term test) -0.5154997829966561 Finished! diff ( y , x , 1 ) = arctan ( 0.1 * x + 0.2 ) ; Iterations 40001 Total Elapsed Time 1 Minutes 14 Seconds Elapsed Time(since restart) 1 Minutes 14 Seconds Time to Timeout 28 Minutes 46.0 Seconds Percent Done 100.00499999954486%