##############ECHO OF PROBLEM#################
##############temp/expt_lin_sin_new_sm_hpostode.ode#################
diff  (  y  ,  x  ,  1  )   =  expt  (  2.0  *  x  +  1.0  ,  sin  (  x  )   )   *   (  cos  (  x  )   *  ln  (  2.0 *  x  +  1.0  )  +   (  2.0  *  sin  (  x  )   )   /   (  2.0  *  x  +  1.0  )   )  ; 
!
#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=1.0 
$array_y_init[0 + 1] = exact_soln_y(x_start)
$glob_look_poles=true 
$glob_max_iter=1000000 
$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=10.0 
$glob_subiter_method=3 
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
def exact_soln_y (x)
return(expt(2.0*x+1.0,sin(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
estimated_h                   1.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-10
range                         0.9
estimated_steps               900000.0000000001
step_error                    1.111111111111111e-16
est_needed_step_err           1.111111111111111e-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      1.031890051472423e-152
estimated_step_error          1.031890051472423e-152
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      1.6681238136644625e-144
estimated_step_error          1.6681238136644625e-144
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      1.1194571309197246e-136
estimated_step_error          1.1194571309197246e-136
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      7.512525334680389e-129
estimated_step_error          7.512525334680389e-129
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      5.041537794430847e-121
estimated_step_error          5.041537794430847e-121
best_h                        1.0e-05
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                             0.1 
y[1] (analytic)                  1.0183684460594404 
y[1] (numeric)                   1.0183684460594404 
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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.11000999999999612 
y[1] (analytic)                  1.0220733759927472 
y[1] (numeric)                   1.0220733759945166 
absolute error                   1.7694734566475745e-12 
relative error                   1.731258731721558e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.12000999999999225 
y[1] (analytic)                  1.0260900641274175 
y[1] (numeric)                   1.0260900641291884 
absolute error                   1.7708057242771247e-12 
relative error                   1.7257800130664068e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.13000999999999532 
y[1] (analytic)                  1.030417767205002 
y[1] (numeric)                   1.030417767206771 
absolute error                   1.7688073228327994e-12 
relative error                   1.7165924143861296e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.14000000000000531 
y[1] (analytic)                  1.0350478154533707 
y[1] (numeric)                   1.0350478154551372 
absolute error                   1.766586876783549e-12 
relative error                   1.7067683737970602e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.15000000000001532 
y[1] (analytic)                  1.0399859731534131 
y[1] (numeric)                   1.039985973155176 
absolute error                   1.7628121184998236e-12 
relative error                   1.6950345139316442e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.16000000000002532 
y[1] (analytic)                  1.045224599813295 
y[1] (numeric)                   1.0452245998150544 
absolute error                   1.759481449425948e-12 
relative error                   1.6833525059975037e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.17000000000003532 
y[1] (analytic)                  1.0507608625916391 
y[1] (numeric)                   1.0507608625933904 
absolute error                   1.751265799043722e-12 
relative error                   1.6666644727557982e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.18000000000004532 
y[1] (analytic)                  1.056592232838107 
y[1] (numeric)                   1.0565922328398512 
absolute error                   1.744160371686121e-12 
relative error                   1.6507412391260352e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.19000000000005532 
y[1] (analytic)                  1.06271646596987 
y[1] (numeric)                   1.0627164659716082 
absolute error                   1.738165167353145e-12 
relative error                   1.6355869350032497e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.20000000000006532 
y[1] (analytic)                  1.0691315827959662 
y[1] (numeric)                   1.0691315827977 
absolute error                   1.7337242752546445e-12 
relative error                   1.6216191749949544e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.21000000000007532 
y[1] (analytic)                  1.0758358521486366 
y[1] (numeric)                   1.0758358521503666 
absolute error                   1.729949516970919e-12 
relative error                   1.608005081366177e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.22000000000008532 
y[1] (analytic)                  1.0828277746952788 
y[1] (numeric)                   1.082827774697001 
absolute error                   1.7221779557985428e-12 
relative error                   1.590444940593794e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.23000000000009532 
y[1] (analytic)                  1.0901060678174883 
y[1] (numeric)                   1.0901060678192025 
absolute error                   1.7141843500212417e-12 
relative error                   1.572493173488362e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.24000000000010532 
y[1] (analytic)                  1.0976696514550293 
y[1] (numeric)                   1.0976696514567363 
absolute error                   1.7070789226636407e-12 
relative error                   1.555184586182921e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.2500000000001153 
y[1] (analytic)                  1.1055176348226559 
y[1] (numeric)                   1.105517634824356 
absolute error                   1.7001955399109647e-12 
relative error                   1.5379180633185516e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.2600000000001253 
y[1] (analytic)                  1.113649303916657 
y[1] (numeric)                   1.1136493039183482 
absolute error                   1.6910917111090384e-12 
relative error                   1.5185136875329972e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.2700000000001353 
y[1] (analytic)                  1.122064109735975 
y[1] (numeric)                   1.122064109737654 
absolute error                   1.6791013024430868e-12 
relative error                   1.4964397202207852e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.2800000000001453 
y[1] (analytic)                  1.130761657149848 
y[1] (numeric)                   1.130761657151516 
absolute error                   1.6679990721968352e-12 
relative error                   1.4751111002482397e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.2900000000001553 
y[1] (analytic)                  1.1397416943502796 
y[1] (numeric)                   1.1397416943519407 
absolute error                   1.6611156894441592e-12 
relative error                   1.457449260370433e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.3000000000001653 
y[1] (analytic)                  1.149004102833311 
y[1] (numeric)                   1.1490041028349611 
absolute error                   1.6502355038028327e-12 
relative error                   1.4362311672634965e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.3100000000001753 
y[1] (analytic)                  1.158548887858167 
y[1] (numeric)                   1.15854888785981 
absolute error                   1.6431300764452317e-12 
relative error                   1.4182656370098633e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.3200000000001853 
y[1] (analytic)                  1.1683761693379184 
y[1] (numeric)                   1.168376169339554 
absolute error                   1.6355805598777806e-12 
relative error                   1.3998749741742953e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.3300000000001953 
y[1] (analytic)                  1.1784861731194074 
y[1] (numeric)                   1.178486173121033 
absolute error                   1.6255885526561542e-12 
relative error                   1.379387038842623e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.3400000000002053 
y[1] (analytic)                  1.1888792226138918 
y[1] (numeric)                   1.1888792226155074 
absolute error                   1.6155965454345278e-12 
relative error                   1.3589240308888966e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.3500000000002153 
y[1] (analytic)                  1.1995557307432132 
y[1] (numeric)                   1.199555730744818 
absolute error                   1.6047163597932013e-12 
relative error                   1.3377589041227464e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.3600000000002253 
y[1] (analytic)                  1.2105161921693084 
y[1] (numeric)                   1.2105161921708973 
absolute error                   1.588951192843524e-12 
relative error                   1.312622832410065e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.3700000000002353 
y[1] (analytic)                  1.2217611757776348 
y[1] (numeric)                   1.2217611757792153 
absolute error                   1.5805134978563729e-12 
relative error                   1.2936353922446398e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.3800000000002453 
y[1] (analytic)                  1.2332913173875661 
y[1] (numeric)                   1.2332913173891351 
absolute error                   1.5689671784002712e-12 
relative error                   1.2721788893509397e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.3900000000002553 
y[1] (analytic)                  1.2451073126650811 
y[1] (numeric)                   1.2451073126666392 
absolute error                   1.5580869927589447e-12 
relative error                   1.251367634669134e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.4000000000002653 
y[1] (analytic)                  1.2572099102151315 
y[1] (numeric)                   1.2572099102166794 
absolute error                   1.5478729409323932e-12 
relative error                   1.2311968974755567e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.4100000000002753 
y[1] (analytic)                  1.2695999048329725 
y[1] (numeric)                   1.2695999048345112 
absolute error                   1.538769112130467e-12 
relative error                   1.2120110487349998e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.4200000000002853 
y[1] (analytic)                  1.2822781308954565 
y[1] (numeric)                   1.2822781308969815 
absolute error                   1.525002346625115e-12 
relative error                   1.1892913946525443e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.4300000000002953 
y[1] (analytic)                  1.2952454558748916 
y[1] (numeric)                   1.2952454558764075 
absolute error                   1.5158985178231887e-12 
relative error                   1.1703561753082963e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.4400000000003053 
y[1] (analytic)                  1.3085027739595216 
y[1] (numeric)                   1.3085027739610235 
absolute error                   1.5019097077129118e-12 
relative error                   1.1478078133286197e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.4500000000003153 
y[1] (analytic)                  1.3220509997660377 
y[1] (numeric)                   1.322050999767523 
absolute error                   1.4852563623435344e-12 
relative error                   1.1234486132580203e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.4600000000003253 
y[1] (analytic)                  1.3358910621307836 
y[1] (numeric)                   1.3358910621322548 
absolute error                   1.4712675522332574e-12 
relative error                   1.1013379712912703e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.4700000000003353 
y[1] (analytic)                  1.350023897967471 
y[1] (numeric)                   1.350023897968923 
absolute error                   1.4519496716047797e-12 
relative error                   1.0754992365622291e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.4800000000003453 
y[1] (analytic)                  1.3644504461803098 
y[1] (numeric)                   1.3644504461817455 
absolute error                   1.4357404154452524e-12 
relative error                   1.0522481189877685e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.4900000000003553 
y[1] (analytic)                  1.3791716416224615 
y[1] (numeric)                   1.3791716416238824 
absolute error                   1.4208634269152753e-12 
relative error                   1.03022958421895e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.5000000000003653 
y[1] (analytic)                  1.3941884090906707 
y[1] (numeric)                   1.3941884090920766 
absolute error                   1.4059864383852982e-12 
relative error                   1.0084622919095437e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.5100000000003198 
y[1] (analytic)                  1.4095016573477332 
y[1] (numeric)                   1.409501657349205 
absolute error                   1.4717116414431075e-12 
relative error                   1.0441361553362307e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.5200000000002742 
y[1] (analytic)                  1.425112273165809 
y[1] (numeric)                   1.4251122731673542 
absolute error                   1.5452084056732929e-12 
relative error                   1.0842713481378536e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.5300000000002287 
y[1] (analytic)                  1.4410211153831056 
y[1] (numeric)                   1.4410211153847203 
absolute error                   1.6147083670148277e-12 
relative error                   1.1205306777101223e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.5400000000001832 
y[1] (analytic)                  1.4572290089689028 
y[1] (numeric)                   1.4572290089705957 
absolute error                   1.6928680679484387e-12 
relative error                   1.1617035191649581e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.5500000000001377 
y[1] (analytic)                  1.4737367390913374 
y[1] (numeric)                   1.4737367390931033 
absolute error                   1.765920742968774e-12 
relative error                   1.1982606500382073e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.5600000000000922 
y[1] (analytic)                  1.4905450451835645 
y[1] (numeric)                   1.490545045185406 
absolute error                   1.8416379532482097e-12 
relative error                   1.2355466607326902e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.5700000000000467 
y[1] (analytic)                  1.5076546150044718 
y[1] (numeric)                   1.5076546150063939 
absolute error                   1.922018100231071e-12 
relative error                   1.2748397949389557e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.5800000000000012 
y[1] (analytic)                  1.5250660786907668 
y[1] (numeric)                   1.5250660786927668 
absolute error                   1.999955756559757e-12 
relative error                   1.311389574854797e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.5900099999999556 
y[1] (analytic)                  1.5427978682754115 
y[1] (numeric)                   1.542797868277491 
absolute error                   2.079447725122918e-12 
relative error                   1.3478419745597593e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.6000099999999101 
y[1] (analytic)                  1.560815052986506 
y[1] (numeric)                   1.5608150529886673 
absolute error                   2.1613821843402548e-12 
relative error                   1.384777895500564e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.6100099999998646 
y[1] (analytic)                  1.5791356169630002 
y[1] (numeric)                   1.579135616965246 
absolute error                   2.2457591342117666e-12 
relative error                   1.4221445644616766e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.6200099999998191 
y[1] (analytic)                  1.5977599000385232 
y[1] (numeric)                   1.5977599000408533 
absolute error                   2.3301360840832785e-12 
relative error                   1.4583768712852895e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.6300099999997736 
y[1] (analytic)                  1.6166881544794194 
y[1] (numeric)                   1.6166881544818354 
absolute error                   2.4160673461892657e-12 
relative error                   1.4944547836853853e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.6400099999997281 
y[1] (analytic)                  1.6359205389508757 
y[1] (numeric)                   1.6359205389533795 
absolute error                   2.503774965134653e-12 
relative error                   1.5304991321524312e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.6500099999996826 
y[1] (analytic)                  1.6554571124681527 
y[1] (numeric)                   1.6554571124707442 
absolute error                   2.5914825840800404e-12 
relative error                   1.5654181340985328e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.660009999999637 
y[1] (analytic)                  1.6752978283341464 
y[1] (numeric)                   1.6752978283368276 
absolute error                   2.681188604469753e-12 
relative error                   1.6004250462950977e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.6700099999995915 
y[1] (analytic)                  1.695442528065001 
y[1] (numeric)                   1.6954425280677732 
absolute error                   2.772226892489016e-12 
relative error                   1.6351051991440506e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.680009999999546 
y[1] (analytic)                  1.715890935305978 
y[1] (numeric)                   1.7158909353088465 
absolute error                   2.8685942510264795e-12 
relative error                   1.671781225719309e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.6900099999995005 
y[1] (analytic)                  1.7366426497402723 
y[1] (numeric)                   1.7366426497432343 
absolute error                   2.9620750296999176e-12 
relative error                   1.7056330098439755e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.700009999999455 
y[1] (analytic)                  1.7576971409939333 
y[1] (numeric)                   1.7576971409969921 
absolute error                   3.0588864774472313e-12 
relative error                   1.7402807378508385e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.7100099999994095 
y[1] (analytic)                  1.7790537425405173 
y[1] (numeric)                   1.7790537425436717 
absolute error                   3.1543656575649948e-12 
relative error                   1.7730581050691084e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.720009999999364 
y[1] (analytic)                  1.8007116456095547 
y[1] (numeric)                   1.8007116456128067 
absolute error                   3.2520652837320085e-12 
relative error                   1.8059889220248584e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.7300099999993185 
y[1] (analytic)                  1.8226698931033676 
y[1] (numeric)                   1.8226698931067227 
absolute error                   3.355093980417223e-12 
relative error                   1.8407578866103257e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.740009999999273 
y[1] (analytic)                  1.8449273735272158 
y[1] (numeric)                   1.8449273735306704 
absolute error                   3.454569963423637e-12 
relative error                   1.872469351906809e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.7500099999992275 
y[1] (analytic)                  1.8674828149381932 
y[1] (numeric)                   1.867482814941749 
absolute error                   3.5558223032694514e-12 
relative error                   1.9040723024737103e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.760009999999182 
y[1] (analytic)                  1.8903347789187184 
y[1] (numeric)                   1.8903347789223792 
absolute error                   3.660849401398991e-12 
relative error                   1.9366143194450544e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.7700099999991364 
y[1] (analytic)                  1.9134816545808944 
y[1] (numeric)                   1.9134816545846578 
absolute error                   3.763434008874356e-12 
relative error                   1.9667991066779537e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.7800099999990909 
y[1] (analytic)                  1.9369216526084256 
y[1] (numeric)                   1.9369216526123 
absolute error                   3.874456311336871e-12 
relative error                   2.00031648472678e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.7900099999990454 
y[1] (analytic)                  1.9606527993431868 
y[1] (numeric)                   1.9606527993471687 
absolute error                   3.9819259001205864e-12 
relative error                   2.0309184275025748e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.8000099999989999 
y[1] (analytic)                  1.9846729309239373 
y[1] (numeric)                   1.9846729309280273 
absolute error                   4.090061622719077e-12 
relative error                   2.060824007316412e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.8100099999989544 
y[1] (analytic)                  2.0089796874850667 
y[1] (numeric)                   2.008979687489266 
absolute error                   4.199307568342192e-12 
relative error                   2.0902688038618642e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.8200099999989089 
y[1] (analytic)                  2.0335705074236348 
y[1] (numeric)                   2.0335705074279375 
absolute error                   4.302780354237257e-12 
relative error                   2.1158746837298122e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.8300099999988634 
y[1] (analytic)                  2.0584426217433354 
y[1] (numeric)                   2.0584426217477483 
absolute error                   4.412914478280072e-12 
relative error                   2.143812235360094e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.8400099999988179 
y[1] (analytic)                  2.0835930484843797 
y[1] (numeric)                   2.0835930484889054 
absolute error                   4.525713137581988e-12 
relative error                   2.1720715284945033e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.8500099999987724 
y[1] (analytic)                  2.10901858724863 
y[1] (numeric)                   2.1090185872532694 
absolute error                   4.639399975303604e-12 
relative error                   2.1997909375260856e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.8600099999987268 
y[1] (analytic)                  2.13471581382965 
y[1] (numeric)                   2.1347158138344042 
absolute error                   4.75441908065477e-12 
relative error                   2.2271906404840887e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.8700099999986813 
y[1] (analytic)                  2.160681074957659 
y[1] (numeric)                   2.1606810749625316 
absolute error                   4.872546810474887e-12 
relative error                   2.2550976481202206e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.8800099999986358 
y[1] (analytic)                  2.1869104831696777 
y[1] (numeric)                   2.1869104831746764 
absolute error                   4.998668146072305e-12 
relative error                   2.2857214250613975e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.8900099999985903 
y[1] (analytic)                  2.2133999118154306 
y[1] (numeric)                   2.2133999118205505 
absolute error                   5.119904500361372e-12 
relative error                   2.3131402838821052e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.9000099999985448 
y[1] (analytic)                  2.2401449902098625 
y[1] (numeric)                   2.240144990215109 
absolute error                   5.24646992516864e-12 
relative error                   2.342022479838297e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.9100099999984993 
y[1] (analytic)                  2.2671410989433447 
y[1] (numeric)                   2.267141098948712 
absolute error                   5.367262190247857e-12 
relative error                   2.3674142702231447e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.9200099999984538 
y[1] (analytic)                  2.2943833653609085 
y[1] (numeric)                   2.2943833653663903 
absolute error                   5.481837206389173e-12 
relative error                   2.3892420460984626e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.9300099999984083 
y[1] (analytic)                  2.3218666592220334 
y[1] (numeric)                   2.3218666592276476 
absolute error                   5.6141757909244916e-12 
relative error                   2.4179578825622923e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.9400099999983628 
y[1] (analytic)                  2.349585588552716 
y[1] (numeric)                   2.3495855885584547 
absolute error                   5.738520769682509e-12 
relative error                   2.4423544294963474e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.9500099999983173 
y[1] (analytic)                  2.377534495701708 
y[1] (numeric)                   2.3775344957075712 
absolute error                   5.863309837650377e-12 
relative error                   2.4661302909591955e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.9600099999982717 
y[1] (analytic)                  2.4057074536129575 
y[1] (numeric)                   2.4057074536189407 
absolute error                   5.983213924309894e-12 
relative error                   2.487091236020464e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.9700099999982262 
y[1] (analytic)                  2.4340982623263945 
y[1] (numeric)                   2.4340982623324976 
absolute error                   6.1031180109694105e-12 
relative error                   2.5073424953421323e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.9800099999981807 
y[1] (analytic)                  2.4627004457193094 
y[1] (numeric)                   2.4627004457255457 
absolute error                   6.236344773924429e-12 
relative error                   2.532319667527777e-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
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.9900099999981352 
y[1] (analytic)                  2.4915072485006156 
y[1] (numeric)                   2.4915072485069834 
absolute error                   6.367795180040048e-12 
relative error                   2.5558003830300613e-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
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff  (  y  ,  x  ,  1  )   =  expt  (  2.0  *  x  +  1.0  ,  sin  (  x  )   )   *   (  cos  (  x  )   *  ln  (  2.0 *  x  +  1.0  )  +   (  2.0  *  sin  (  x  )   )   /   (  2.0  *  x  +  1.0  )   )  ; 
Iterations                      90001 
Total Elapsed Time              2 Minutes 57 Seconds
Elapsed Time(since restart)     2 Minutes 57 Seconds
Time to Timeout                 7 Minutes 3.0 Seconds
Percent Done                    100.00222222200998%