##############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=c(-1.0) x_end=c(-0.6) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=0 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=8 $glob_max_minutes=(3.0) $glob_subiter_method=3 $glob_max_iter=100000 $glob_upper_ratio_limit=c(1.000001) $glob_lower_ratio_limit=c(0.999999) $glob_look_poles=false $glob_h=c(0.001) $glob_display_interval=c(0.01) #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arctan(c(0.1) * c(x) + c(0.2))-c(5.0) * ln(c(1.0) + expt((c(0.1) * c(x) + c(0.2)) , c(2)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] -1.0 y[1] (closed_form) 0.04991699822532158 y[1] (numeric) 0.04991699822532158 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.99 y[1] (closed_form) 0.050918634917733505 y[1] (numeric) 0.05091863492429724 absolute error 6.56373566609858e-12 relative error 1.2890635573210582e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] -0.98 y[1] (closed_form) 0.05193017062867282 y[1] (numeric) 0.0519301706418644 absolute error 1.319157977297536e-11 relative error 2.5402535006676324e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] -0.97 y[1] (closed_form) 0.052951603369334195 y[1] (numeric) 0.05295160338921538 absolute error 1.9881186974490817e-11 relative error 3.754595840246943e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] -0.96 y[1] (closed_form) 0.05398293113212667 y[1] (numeric) 0.0539829311587592 absolute error 2.6632529515069336e-11 relative error 4.933509343885852e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] -0.95 y[1] (closed_form) 0.05502415189069715 y[1] (numeric) 0.05502415192414486 absolute error 3.34477098795638e-11 relative error 6.078732471153046e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] -0.94 y[1] (closed_form) 0.05607526359996047 y[1] (numeric) 0.05607526364028493 absolute error 4.032445904966764e-11 relative error 7.191131429598141e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] -0.9299999999999999 y[1] (closed_form) 0.057136264196115505 y[1] (numeric) 0.05713626424337928 absolute error 4.7263776226103005e-11 relative error 8.272115247835245e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] -0.9199999999999999 y[1] (closed_form) 0.05820715159667454 y[1] (numeric) 0.058207151650939065 absolute error 5.426452343026966e-11 relative error 9.322655711840377e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h 0.001 TOP MAIN SOLVE Loop x[1] -0.9099999999999999 y[1] (closed_form) 0.059287923700482026 y[1] (numeric) 0.059287923761810794 absolute error 6.132876845255097e-11 relative error 1.034422604548932e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.8999999999999999 y[1] (closed_form) 0.06037857838774653 y[1] (numeric) 0.0603785784562008 absolute error 6.845427003021598e-11 relative error 1.1337509404512306e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.8899999999999999 y[1] (closed_form) 0.06147911352005771 y[1] (numeric) 0.061479113595699714 absolute error 7.564200654730513e-11 relative error 1.230369180951621e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.8799999999999999 y[1] (closed_form) 0.06258952694041534 y[1] (numeric) 0.06258952702330728 absolute error 8.28919433093489e-11 relative error 1.3243740184881297e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.8699999999999999 y[1] (closed_form) 0.06370981647325438 y[1] (numeric) 0.06370981656345723 absolute error 9.02028451932324e-11 relative error 1.41583903684764e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.8599999999999999 y[1] (closed_form) 0.06483997992446676 y[1] (numeric) 0.06483998002204251 absolute error 9.757575303304122e-11 relative error 1.5048701919203082e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.8499999999999999 y[1] (closed_form) 0.06598001508143005 y[1] (numeric) 0.06598001518644066 absolute error 1.0501061131762413e-10 relative error 1.5915517931910745e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.8399999999999999 y[1] (closed_form) 0.06712991971303305 y[1] (numeric) 0.06712991982553923 absolute error 1.1250618492386621e-10 relative error 1.675946960830694e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.8299999999999998 y[1] (closed_form) 0.068289691569697 y[1] (numeric) 0.06828969168976161 absolute error 1.200646110310899e-10 relative error 1.7581659584529095e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.8199999999999998 y[1] (closed_form) 0.06945932838340939 y[1] (numeric) 0.06945932851109299 absolute error 1.2768359980430688e-10 relative error 1.8382498474431632e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.8099999999999998 y[1] (closed_form) 0.0706388278677423 y[1] (numeric) 0.07063882800310646 absolute error 1.3536416432202714e-10 relative error 1.9162855388182638e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.7999999999999998 y[1] (closed_form) 0.07182818771788424 y[1] (numeric) 0.0718281878609893 absolute error 1.4310505558334796e-10 relative error 1.9923244638360375e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.7899999999999998 y[1] (closed_form) 0.07302740561066216 y[1] (numeric) 0.07302740576156959 absolute error 1.509074254446574e-10 relative error 2.066449221121236e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.7799999999999998 y[1] (closed_form) 0.07423647920457176 y[1] (numeric) 0.07423647936334281 absolute error 1.5877105186135054e-10 relative error 2.138720122001325e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.7699999999999998 y[1] (closed_form) 0.07545540613980296 y[1] (numeric) 0.07545540630649884 absolute error 1.6669587932227614e-10 relative error 2.2091972974530653e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.7599999999999998 y[1] (closed_form) 0.07668418403826716 y[1] (numeric) 0.07668418421294901 absolute error 1.7468185231628297e-10 relative error 2.2779384628923317e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.7499999999999998 y[1] (closed_form) 0.0779228105036256 y[1] (numeric) 0.07792281068635337 absolute error 1.8272777735361956e-10 relative error 2.344984429753308e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.7399999999999998 y[1] (closed_form) 0.07917128312131357 y[1] (numeric) 0.07917128331214819 absolute error 1.9083462587943245e-10 relative error 2.410402084642458e-07% Desired digits 8 Estimated correct digits 12 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.7299999999999998 y[1] (closed_form) 0.08042959945857128 y[1] (numeric) 0.08042959965757361 absolute error 1.990023285047826e-10 relative error 2.4742424411461517e-07% Desired digits 8 Estimated correct digits 12 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.7199999999999998 y[1] (closed_form) 0.08169775706447183 y[1] (numeric) 0.0816977572717015 absolute error 2.0722967786213076e-10 relative error 2.536540601703366e-07% Desired digits 8 Estimated correct digits 12 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.7099999999999997 y[1] (closed_form) 0.08297575346994582 y[1] (numeric) 0.0829757536854635 absolute error 2.1551768702998686e-10 relative error 2.597357396797226e-07% Desired digits 8 Estimated correct digits 12 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6999999999999997 y[1] (closed_form) 0.08426358618781293 y[1] (numeric) 0.08426358641167916 absolute error 2.2386623110826065e-10 relative error 2.6567375213451156e-07% Desired digits 8 Estimated correct digits 12 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6899999999999997 y[1] (closed_form) 0.08556125271280927 y[1] (numeric) 0.08556125294508456 absolute error 2.322752823413765e-10 relative error 2.7147251235441864e-07% Desired digits 8 Estimated correct digits 12 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6799999999999997 y[1] (closed_form) 0.08686875052161584 y[1] (numeric) 0.08686875076236059 absolute error 2.407447435848198e-10 relative error 2.7713618779967887e-07% Desired digits 8 Estimated correct digits 12 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6699999999999997 y[1] (closed_form) 0.08818607707288864 y[1] (numeric) 0.08818607732216198 absolute error 2.4927333808211216e-10 relative error 2.8266745313557795e-07% Desired digits 8 Estimated correct digits 12 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6599999999999997 y[1] (closed_form) 0.08951322980728404 y[1] (numeric) 0.08951323006514617 absolute error 2.5786212054512703e-10 relative error 2.88071518702081e-07% Desired digits 8 Estimated correct digits 12 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6499999999999997 y[1] (closed_form) 0.09085020614749255 y[1] (numeric) 0.0908502064140024 absolute error 2.665098558507495e-10 relative error 2.9335085428213433e-07% Desired digits 8 Estimated correct digits 12 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6399999999999997 y[1] (closed_form) 0.09219700349826254 y[1] (numeric) 0.09219700377348124 absolute error 2.7521869505608976e-10 relative error 2.985115400863069e-07% Desired digits 8 Estimated correct digits 12 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6299999999999997 y[1] (closed_form) 0.09355361924643742 y[1] (numeric) 0.09355361953042374 absolute error 2.8398632057058393e-10 relative error 3.035546062868095e-07% Desired digits 8 Estimated correct digits 12 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6199999999999997 y[1] (closed_form) 0.09492005076097768 y[1] (numeric) 0.09492005105379142 absolute error 2.9281374547274197e-10 relative error 3.0848460691417984e-07% Desired digits 8 Estimated correct digits 12 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6099999999999997 y[1] (closed_form) 0.09629629539299625 y[1] (numeric) 0.09629629569469601 absolute error 3.016997623950246e-10 relative error 3.133036023491384e-07% Desired digits 8 Estimated correct digits 12 Correct digits 9 h 0.001 Finished! diff ( y , x , 1 ) = arctan ( 0.1 * x + 0.2 ) ; Iterations 400 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.25000000000009%