##############ECHO OF PROBLEM################# ##############temp/add_c_linpostode.ode################# diff ( y , x , 1 ) = 0.3 + ( 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(0.1) x_end=c(1.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_display_interval=c(0.1) $glob_look_poles=true $glob_min_h=c(0.1) # 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=3 #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=true $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(0.05) * c(x) * c(x) + c(0.5) * c(x)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 0.0505 y[1] (numeric) 0.0505 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 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] 0.11000000000000001 y[1] (closed_form) 0.05560500000000001 y[1] (numeric) 0.055605 absolute error 6.938893903907228e-18 relative error 1.2478902803537861e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.12000000000000002 y[1] (closed_form) 0.06072000000000001 y[1] (numeric) 0.060719999999999996 absolute error 1.3877787807814457e-17 relative error 2.285538176517532e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.13000000000000003 y[1] (closed_form) 0.06584500000000001 y[1] (numeric) 0.065845 absolute error 1.3877787807814457e-17 relative error 2.1076448944968415e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.14000000000000004 y[1] (closed_form) 0.07098000000000002 y[1] (numeric) 0.07098 absolute error 1.3877787807814457e-17 relative error 1.955168752861997e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.15000000000000005 y[1] (closed_form) 0.07612500000000003 y[1] (numeric) 0.076125 absolute error 2.7755575615628914e-17 relative error 3.646052626026785e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.16000000000000006 y[1] (closed_form) 0.08128000000000003 y[1] (numeric) 0.08128 absolute error 2.7755575615628914e-17 relative error 3.4148099920803275e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.17000000000000007 y[1] (closed_form) 0.08644500000000004 y[1] (numeric) 0.08644500000000001 absolute error 2.7755575615628914e-17 relative error 3.2107786009172196e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.18000000000000008 y[1] (closed_form) 0.09162000000000003 y[1] (numeric) 0.09162000000000001 absolute error 2.7755575615628914e-17 relative error 3.029423228075628e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.19000000000000009 y[1] (closed_form) 0.09680500000000004 y[1] (numeric) 0.09680500000000002 absolute error 2.7755575615628914e-17 relative error 2.8671634332554003e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.2000000000000001 y[1] (closed_form) 0.10200000000000005 y[1] (numeric) 0.10200000000000002 absolute error 2.7755575615628914e-17 relative error 2.721134864277343e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.2100000000000001 y[1] (closed_form) 0.10720500000000005 y[1] (numeric) 0.10720500000000002 absolute error 2.7755575615628914e-17 relative error 2.589018759911282e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.2200000000000001 y[1] (closed_form) 0.11242000000000006 y[1] (numeric) 0.11242000000000002 absolute error 4.163336342344337e-17 relative error 3.7033769278992483e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.23000000000000012 y[1] (closed_form) 0.11764500000000007 y[1] (numeric) 0.11764500000000001 absolute error 5.551115123125783e-17 relative error 4.718530428939419e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.24000000000000013 y[1] (closed_form) 0.12288000000000007 y[1] (numeric) 0.12288000000000002 absolute error 5.551115123125783e-17 relative error 4.517509052022932e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.2500000000000001 y[1] (closed_form) 0.12812500000000004 y[1] (numeric) 0.12812500000000002 absolute error 2.7755575615628914e-17 relative error 2.1662888285368902e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.2600000000000001 y[1] (closed_form) 0.13338000000000005 y[1] (numeric) 0.13338000000000003 absolute error 2.7755575615628914e-17 relative error 2.0809398422273882e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.27000000000000013 y[1] (closed_form) 0.13864500000000007 y[1] (numeric) 0.13864500000000002 absolute error 5.551115123125783e-17 relative error 4.0038336204881385e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.28000000000000014 y[1] (closed_form) 0.14392000000000008 y[1] (numeric) 0.14392000000000002 absolute error 5.551115123125783e-17 relative error 3.857083882105183e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.29000000000000015 y[1] (closed_form) 0.1492050000000001 y[1] (numeric) 0.14920500000000003 absolute error 5.551115123125783e-17 relative error 3.7204618632926376e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.30000000000000016 y[1] (closed_form) 0.15450000000000008 y[1] (numeric) 0.15450000000000003 absolute error 5.551115123125783e-17 relative error 3.5929547722496957e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.31000000000000016 y[1] (closed_form) 0.15980500000000009 y[1] (numeric) 0.15980500000000003 absolute error 5.551115123125783e-17 relative error 3.473680500063064e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.3200000000000002 y[1] (closed_form) 0.1651200000000001 y[1] (numeric) 0.16512000000000004 absolute error 5.551115123125783e-17 relative error 3.361867201505438e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.3300000000000002 y[1] (closed_form) 0.1704450000000001 y[1] (numeric) 0.17044500000000004 absolute error 5.551115123125783e-17 relative error 3.2568365884160753e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.3400000000000002 y[1] (closed_form) 0.1757800000000001 y[1] (numeric) 0.17578000000000005 absolute error 5.551115123125783e-17 relative error 3.157990171308328e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.3500000000000002 y[1] (closed_form) 0.18112500000000012 y[1] (numeric) 0.18112500000000006 absolute error 5.551115123125783e-17 relative error 3.0647978595587464e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.3600000000000002 y[1] (closed_form) 0.18648000000000012 y[1] (numeric) 0.18648000000000006 absolute error 5.551115123125783e-17 relative error 2.9767884615646606e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.3700000000000002 y[1] (closed_form) 0.19184500000000013 y[1] (numeric) 0.19184500000000007 absolute error 5.551115123125783e-17 relative error 2.8935417254167575e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.3800000000000002 y[1] (closed_form) 0.19722000000000012 y[1] (numeric) 0.19722000000000006 absolute error 5.551115123125783e-17 relative error 2.814681636307565e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.39000000000000024 y[1] (closed_form) 0.20260500000000012 y[1] (numeric) 0.20260500000000006 absolute error 5.551115123125783e-17 relative error 2.73987074510786e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.40000000000000024 y[1] (closed_form) 0.20800000000000013 y[1] (numeric) 0.20800000000000007 absolute error 5.551115123125783e-17 relative error 2.6688053476566247e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.41000000000000025 y[1] (closed_form) 0.21340500000000015 y[1] (numeric) 0.21340500000000007 absolute error 8.326672684688674e-17 relative error 3.9018170542811404e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.42000000000000026 y[1] (closed_form) 0.21882000000000015 y[1] (numeric) 0.21882000000000007 absolute error 8.326672684688674e-17 relative error 3.805261257969412e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.43000000000000027 y[1] (closed_form) 0.22424500000000014 y[1] (numeric) 0.22424500000000006 absolute error 8.326672684688674e-17 relative error 3.713203275296514e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.4400000000000003 y[1] (closed_form) 0.22968000000000016 y[1] (numeric) 0.22968000000000005 absolute error 1.1102230246251565e-16 relative error 4.8337818905658124e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.4500000000000003 y[1] (closed_form) 0.23512500000000017 y[1] (numeric) 0.23512500000000006 absolute error 1.1102230246251565e-16 relative error 4.7218416783632355e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.4600000000000003 y[1] (closed_form) 0.24058000000000015 y[1] (numeric) 0.24058000000000004 absolute error 1.1102230246251565e-16 relative error 4.614776891783007e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.4700000000000003 y[1] (closed_form) 0.24604500000000018 y[1] (numeric) 0.24604500000000004 absolute error 1.3877787807814457e-16 relative error 5.6403453871505e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.4800000000000003 y[1] (closed_form) 0.2515200000000002 y[1] (numeric) 0.2515200000000001 absolute error 1.1102230246251565e-16 relative error 4.4140546462514145e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.4900000000000003 y[1] (closed_form) 0.2570050000000002 y[1] (numeric) 0.257005 absolute error 2.220446049250313e-16 relative error 8.639699808370698e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.5000000000000003 y[1] (closed_form) 0.2625000000000002 y[1] (numeric) 0.26250000000000007 absolute error 1.1102230246251565e-16 relative error 4.2294210461910695e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.5100000000000003 y[1] (closed_form) 0.2680050000000002 y[1] (numeric) 0.268005 absolute error 2.220446049250313e-16 relative error 8.285091879816836e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.5200000000000004 y[1] (closed_form) 0.2735200000000002 y[1] (numeric) 0.2735200000000001 absolute error 1.1102230246251565e-16 relative error 4.059019540162166e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.5300000000000004 y[1] (closed_form) 0.2790450000000002 y[1] (numeric) 0.279045 absolute error 2.220446049250313e-16 relative error 7.95730455392611e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.5400000000000004 y[1] (closed_form) 0.2845800000000002 y[1] (numeric) 0.2845800000000001 absolute error 1.1102230246251565e-16 relative error 3.9012686226198454e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.5500000000000004 y[1] (closed_form) 0.2901250000000002 y[1] (numeric) 0.29012499999999997 absolute error 2.220446049250313e-16 relative error 7.653411630332828e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.5600000000000004 y[1] (closed_form) 0.2956800000000002 y[1] (numeric) 0.2956800000000001 absolute error 1.1102230246251565e-16 relative error 3.7548127185645147e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.5700000000000004 y[1] (closed_form) 0.3012450000000002 y[1] (numeric) 0.301245 absolute error 2.220446049250313e-16 relative error 7.370897605770424e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.5800000000000004 y[1] (closed_form) 0.3068200000000002 y[1] (numeric) 0.3068200000000001 absolute error 1.1102230246251565e-16 relative error 3.618483229988774e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.5900000000000004 y[1] (closed_form) 0.3124050000000002 y[1] (numeric) 0.312405 absolute error 2.220446049250313e-16 relative error 7.107588064372567e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.6000000000000004 y[1] (closed_form) 0.3180000000000002 y[1] (numeric) 0.31800000000000006 absolute error 1.6653345369377348e-16 relative error 5.2369010595526215e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.6100000000000004 y[1] (closed_form) 0.32360500000000025 y[1] (numeric) 0.323605 absolute error 2.7755575615628914e-16 relative error 8.576992202107165e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.6200000000000004 y[1] (closed_form) 0.32922000000000023 y[1] (numeric) 0.32922000000000007 absolute error 1.6653345369377348e-16 relative error 5.0584245700070884e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.6300000000000004 y[1] (closed_form) 0.3348450000000002 y[1] (numeric) 0.334845 absolute error 2.220446049250313e-16 relative error 6.631265359346299e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.6400000000000005 y[1] (closed_form) 0.3404800000000003 y[1] (numeric) 0.34048000000000006 absolute error 2.220446049250313e-16 relative error 6.521516826980473e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.6500000000000005 y[1] (closed_form) 0.34612500000000024 y[1] (numeric) 0.346125 absolute error 2.220446049250313e-16 relative error 6.415156516432825e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.6600000000000005 y[1] (closed_form) 0.35178000000000026 y[1] (numeric) 0.35178000000000004 absolute error 2.220446049250313e-16 relative error 6.312030386179747e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.6700000000000005 y[1] (closed_form) 0.3574450000000003 y[1] (numeric) 0.357445 absolute error 2.7755575615628914e-16 relative error 7.764991989153265e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.6800000000000005 y[1] (closed_form) 0.3631200000000003 y[1] (numeric) 0.36312000000000005 absolute error 2.220446049250313e-16 relative error 6.114909807364814e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.6900000000000005 y[1] (closed_form) 0.36880500000000027 y[1] (numeric) 0.36880500000000005 absolute error 2.220446049250313e-16 relative error 6.020650612790802e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.7000000000000005 y[1] (closed_form) 0.3745000000000003 y[1] (numeric) 0.37450000000000006 absolute error 2.220446049250313e-16 relative error 5.92909492456692e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.7100000000000005 y[1] (closed_form) 0.3802050000000003 y[1] (numeric) 0.38020500000000007 absolute error 2.220446049250313e-16 relative error 5.840128481346409e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.7200000000000005 y[1] (closed_form) 0.3859200000000003 y[1] (numeric) 0.38592000000000004 absolute error 2.7755575615628914e-16 relative error 7.192054212175811e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.7300000000000005 y[1] (closed_form) 0.3916450000000003 y[1] (numeric) 0.3916450000000001 absolute error 2.220446049250313e-16 relative error 5.669537589527024e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.7400000000000005 y[1] (closed_form) 0.3973800000000003 y[1] (numeric) 0.39738 absolute error 2.7755575615628914e-16 relative error 6.98464331763775e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.7500000000000006 y[1] (closed_form) 0.40312500000000034 y[1] (numeric) 0.40312500000000007 absolute error 2.7755575615628914e-16 relative error 6.885104028683136e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.7600000000000006 y[1] (closed_form) 0.40888000000000035 y[1] (numeric) 0.40888 absolute error 3.3306690738754696e-16 relative error 8.145835144481184e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.7700000000000006 y[1] (closed_form) 0.4146450000000003 y[1] (numeric) 0.4146450000000001 absolute error 2.220446049250313e-16 relative error 5.355053236504266e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.7800000000000006 y[1] (closed_form) 0.42042000000000035 y[1] (numeric) 0.42042 absolute error 3.3306690738754696e-16 relative error 7.922242219388865e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.7900000000000006 y[1] (closed_form) 0.42620500000000033 y[1] (numeric) 0.4262050000000001 absolute error 2.220446049250313e-16 relative error 5.209807602562878e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.8000000000000006 y[1] (closed_form) 0.43200000000000033 y[1] (numeric) 0.432 absolute error 3.3306690738754696e-16 relative error 7.70988211545247e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.8100000000000006 y[1] (closed_form) 0.43780500000000033 y[1] (numeric) 0.4378050000000001 absolute error 2.220446049250313e-16 relative error 5.071769507544024e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.8200000000000006 y[1] (closed_form) 0.44362000000000035 y[1] (numeric) 0.44362 absolute error 3.3306690738754696e-16 relative error 7.50793263125077e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.8300000000000006 y[1] (closed_form) 0.44944500000000037 y[1] (numeric) 0.44944500000000015 absolute error 2.220446049250313e-16 relative error 4.940417735763689e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.8400000000000006 y[1] (closed_form) 0.45528000000000035 y[1] (numeric) 0.45528 absolute error 3.3306690738754696e-16 relative error 7.315649872332339e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.8500000000000006 y[1] (closed_form) 0.4611250000000004 y[1] (numeric) 0.4611250000000001 absolute error 2.7755575615628914e-16 relative error 6.019100160613475e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.8600000000000007 y[1] (closed_form) 0.4669800000000004 y[1] (numeric) 0.46698 absolute error 3.885780586188048e-16 relative error 8.321085670024508e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.8700000000000007 y[1] (closed_form) 0.4728450000000004 y[1] (numeric) 0.4728450000000001 absolute error 2.7755575615628914e-16 relative error 5.869909931505861e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.8800000000000007 y[1] (closed_form) 0.4787200000000004 y[1] (numeric) 0.47872000000000003 absolute error 3.885780586188048e-16 relative error 8.117021612190935e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.8900000000000007 y[1] (closed_form) 0.4846050000000004 y[1] (numeric) 0.4846050000000001 absolute error 2.7755575615628914e-16 relative error 5.72746373141608e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.9000000000000007 y[1] (closed_form) 0.4905000000000004 y[1] (numeric) 0.49050000000000005 absolute error 3.3306690738754696e-16 relative error 6.790354890673735e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.9100000000000007 y[1] (closed_form) 0.49640500000000043 y[1] (numeric) 0.4964050000000001 absolute error 3.3306690738754696e-16 relative error 6.709580028153356e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.9200000000000007 y[1] (closed_form) 0.5023200000000004 y[1] (numeric) 0.50232 absolute error 4.440892098500626e-16 relative error 8.840763056419458e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.9300000000000007 y[1] (closed_form) 0.5082450000000004 y[1] (numeric) 0.508245 absolute error 4.440892098500626e-16 relative error 8.737699531723131e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.9400000000000007 y[1] (closed_form) 0.5141800000000004 y[1] (numeric) 0.51418 absolute error 4.440892098500626e-16 relative error 8.636843320433744e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.9500000000000007 y[1] (closed_form) 0.5201250000000004 y[1] (numeric) 0.520125 absolute error 4.440892098500626e-16 relative error 8.538124678684207e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.9600000000000007 y[1] (closed_form) 0.5260800000000004 y[1] (numeric) 0.52608 absolute error 4.440892098500626e-16 relative error 8.441476768743579e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.9700000000000008 y[1] (closed_form) 0.5320450000000004 y[1] (numeric) 0.532045 absolute error 4.440892098500626e-16 relative error 8.346835509215617e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 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] 0.9800000000000008 y[1] (closed_form) 0.5380200000000005 y[1] (numeric) 0.5380199999999999 absolute error 5.551115123125783e-16 relative error 1.0317674293010999e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 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] 0.9900000000000008 y[1] (closed_form) 0.5440050000000005 y[1] (numeric) 0.544005 absolute error 5.551115123125783e-16 relative error 1.020416195278679e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 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 ) = 0.3 + ( 0.1 * x + 0.2 ) ; Iterations 900 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.11111111111117%