##############ECHO OF PROBLEM#################
##############temp/expt_c_sin_newpostode.ode#################
diff ( y , x , 1 ) = expt ( 2.0 , sin ( x ) ) * cos ( x ) * ln ( 2.0 ) ;
!
/* BEGIN FIRST INPUT BLOCK */
/* # Comment 1 */
Digits=32;
max_terms=30;
/* # Comment 2 */
!
/* END FIRST INPUT BLOCK */
/* BEGIN SECOND INPUT BLOCK */
/* # Comment 3 */
x_start=1.4;
x_end=1.0;
array_y_init[0 + 1] = exact_soln_y(x_start);
glob_look_poles=true;
glob_max_iter=1000000;
/* # Comment 4 */
glob_max_h=0.0001;
/* END SECOND INPUT BLOCK */
/* BEGIN OVERRIDE BLOCK */
glob_desired_digits_correct=10;
glob_display_interval=0.01;
glob_look_poles=true;
glob_max_iter=1000000000;
glob_max_minutes=30.0;
glob_subiter_method=3;
/* END OVERRIDE BLOCK */
!
/* BEGIN USER DEF BLOCK */
/* # Comment 5 */
double exact_soln_y (double x) {
/* # Comment 6 */
return(expt(2.0,sin(x)));
/* # Comment 7 */
}
/* END USER DEF BLOCK */
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
estimated_h = -1e-06
estimated_answer = 1
desired_abs_gbl_error = 1e-10
range = -0.3999999999999999
estimated_steps = 399999.9999999999
step_error = 2.500000000000001e-16
est_needed_step_err = 2.500000000000001e-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 = 1.305604892242639e-167
estimated_step_error = 1.305604892242639e-167
best_h = -0.0001
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (analytic) = 1.979930418515512
y[1] (numeric) = 1.979930418515512
absolute error = 0
relative error = 0 %
Correct digits = 16
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.134
Order of pole (six term test) = 9.69
TOP MAIN SOLVE Loop
x[1] = 1.389900000000001
y[1] (analytic) = 1.977507037037649
y[1] (numeric) = 1.977507022343582
absolute error = 1.469406663012762e-08
relative error = 7.430601436513558e-07 %
Correct digits = 9
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.136
Order of pole (six term test) = 9.702
TOP MAIN SOLVE Loop
x[1] = 1.379900000000002
y[1] (analytic) = 1.974975232951737
y[1] (numeric) = 1.974975202039042
absolute error = 3.091269462629498e-08
relative error = 1.565219356198904e-06 %
Correct digits = 8
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.138
Order of pole (six term test) = 9.714
TOP MAIN SOLVE Loop
x[1] = 1.369900000000003
y[1] (analytic) = 1.972312440009531
y[1] (numeric) = 1.97231239113323
absolute error = 4.8876301006473e-08
relative error = 2.478121620844049e-06 %
Correct digits = 8
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.139
Order of pole (six term test) = 9.725
TOP MAIN SOLVE Loop
x[1] = 1.359900000000004
y[1] (analytic) = 1.969519462715765
y[1] (numeric) = 1.969519394049318
absolute error = 6.866644697289814e-08
relative error = 3.486456888230704e-06 %
Correct digits = 8
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.141
Order of pole (six term test) = 9.735
TOP MAIN SOLVE Loop
x[1] = 1.349900000000005
y[1] (analytic) = 1.966597143224068
y[1] (numeric) = 1.966597052860836
absolute error = 9.036323178612804e-08
relative error = 4.594903033266145e-06 %
Correct digits = 8
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.142
Order of pole (six term test) = 9.745
TOP MAIN SOLVE Loop
x[1] = 1.339900000000007
y[1] (analytic) = 1.963546360841401
y[1] (numeric) = 1.963546246796171
absolute error = 1.140452305925521e-07
relative error = 5.808125179365893e-06 %
Correct digits = 8
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.144
Order of pole (six term test) = 9.754
TOP MAIN SOLVE Loop
x[1] = 1.329900000000008
y[1] (analytic) = 1.960368031511996
y[1] (numeric) = 1.96036789172256
absolute error = 1.397894362487051e-07
relative error = 7.13077514026221e-06 %
Correct digits = 8
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.145
Order of pole (six term test) = 9.762
TOP MAIN SOLVE Loop
x[1] = 1.319900000000009
y[1] (analytic) = 1.957063107281273
y[1] (numeric) = 1.95706293961007
absolute error = 1.676712035880712e-07
relative error = 8.56749089818559e-06 %
Correct digits = 8
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.147
Order of pole (six term test) = 9.768
TOP MAIN SOLVE Loop
x[1] = 1.30990000000001
y[1] (analytic) = 1.953632575740252
y[1] (numeric) = 1.953632377976061
absolute error = 1.97764191023353e-07
relative error = 1.012289585458095e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.148
Order of pole (six term test) = 9.774
TOP MAIN SOLVE Loop
x[1] = 1.299900000000011
y[1] (analytic) = 1.950077459450965
y[1] (numeric) = 1.95007722931066
absolute error = 2.301403043691863e-07
relative error = 1.180159809826125e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.149
Order of pole (six term test) = 9.778
TOP MAIN SOLVE Loop
x[1] = 1.289900000000012
y[1] (analytic) = 1.946398815353409
y[1] (numeric) = 1.946398550483758
absolute error = 2.648696511009518e-07
relative error = 1.360819011045582e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.15
Order of pole (six term test) = 9.78
TOP MAIN SOLVE Loop
x[1] = 1.279900000000013
y[1] (analytic) = 1.942597734154588
y[1] (numeric) = 1.942597432134107
absolute error = 3.020204808468208e-07
relative error = 1.554724766413151e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.151
Order of pole (six term test) = 9.781
TOP MAIN SOLVE Loop
x[1] = 1.269900000000014
y[1] (analytic) = 1.9386753397002
y[1] (numeric) = 1.938674998041056
absolute error = 3.416591438654137e-07
relative error = 1.762332954202886e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.151
Order of pole (six term test) = 9.781
TOP MAIN SOLVE Loop
x[1] = 1.259900000000015
y[1] (analytic) = 1.934632788329559
y[1] (numeric) = 1.934632404479518
absolute error = 3.838500413078094e-07
relative error = 1.984097672815941e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.152
Order of pole (six term test) = 9.779
TOP MAIN SOLVE Loop
x[1] = 1.249900000000016
y[1] (analytic) = 1.930471268214333
y[1] (numeric) = 1.930470839558751
absolute error = 4.286555819188465e-07
relative error = 2.220471182227688e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.152
Order of pole (six term test) = 9.775
TOP MAIN SOLVE Loop
x[1] = 1.239900000000018
y[1] (analytic) = 1.926191998681697
y[1] (numeric) = 1.926191522545555
absolute error = 4.761361411809162e-07
relative error = 2.471903847107599e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.152
Order of pole (six term test) = 9.769
TOP MAIN SOLVE Loop
x[1] = 1.229900000000019
y[1] (analytic) = 1.921796229522525
y[1] (numeric) = 1.921795703172511
absolute error = 5.263500137964172e-07
relative error = 2.738844034089869e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.152
Order of pole (six term test) = 9.762
TOP MAIN SOLVE Loop
x[1] = 1.21990000000002
y[1] (analytic) = 1.917285240285239
y[1] (numeric) = 1.917284660931855
absolute error = 5.793533841558229e-07
relative error = 3.021738090831134e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.152
Order of pole (six term test) = 9.753
TOP MAIN SOLVE Loop
x[1] = 1.209900000000021
y[1] (analytic) = 1.912660339555944
y[1] (numeric) = 1.912659704355659
absolute error = 6.35200285037385e-07
relative error = 3.321030252474714e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.152
Order of pole (six term test) = 9.742
TOP MAIN SOLVE Loop
x[1] = 1.199900000000022
y[1] (analytic) = 1.907922864225502
y[1] (numeric) = 1.907922170282937
absolute error = 6.939425649665765e-07
relative error = 3.637162581246565e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.151
Order of pole (six term test) = 9.73
TOP MAIN SOLVE Loop
x[1] = 1.189900000000023
y[1] (analytic) = 1.903074178744183
y[1] (numeric) = 1.903073423114324
absolute error = 7.556298591282484e-07
relative error = 3.970574912780752e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.15
Order of pole (six term test) = 9.716
TOP MAIN SOLVE Loop
x[1] = 1.179900000000024
y[1] (analytic) = 1.898115674364571
y[1] (numeric) = 1.898114854055019
absolute error = 8.203095516190473e-07
relative error = 4.321704744857877e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.149
Order of pole (six term test) = 9.701
TOP MAIN SOLVE Loop
x[1] = 1.169900000000025
y[1] (analytic) = 1.893048768373361
y[1] (numeric) = 1.893047880346604
absolute error = 8.880267574618017e-07
relative error = 4.690987217539334e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.148
Order of pole (six term test) = 9.684
TOP MAIN SOLVE Loop
x[1] = 1.159900000000026
y[1] (analytic) = 1.887874903312751
y[1] (numeric) = 1.887873944488458
absolute error = 9.588242930735902e-07
relative error = 5.078855020484102e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.147
Order of pole (six term test) = 9.665
TOP MAIN SOLVE Loop
x[1] = 1.149900000000027
y[1] (analytic) = 1.882595546192068
y[1] (numeric) = 1.882594513449412
absolute error = 1.032742655615593e-06
relative error = 5.485738334527162e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.146
Order of pole (six term test) = 9.645
TOP MAIN SOLVE Loop
x[1] = 1.139900000000029
y[1] (analytic) = 1.877212187690346
y[1] (numeric) = 1.877211077870347
absolute error = 1.10981999834614e-06
relative error = 5.91206473953071e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.145
Order of pole (six term test) = 9.624
TOP MAIN SOLVE Loop
x[1] = 1.12990000000003
y[1] (analytic) = 1.871726341350502
y[1] (numeric) = 1.871725151258388
absolute error = 1.190092114633501e-06
relative error = 6.35825915542128e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.143
Order of pole (six term test) = 9.602
TOP MAIN SOLVE Loop
x[1] = 1.119900000000031
y[1] (analytic) = 1.866139542765825
y[1] (numeric) = 1.8661382691734
absolute error = 1.273592425299341e-06
relative error = 6.824743788515066e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.141
Order of pole (six term test) = 9.579
TOP MAIN SOLVE Loop
x[1] = 1.109900000000032
y[1] (analytic) = 1.860453348759443
y[1] (numeric) = 1.860451988407483
absolute error = 1.360351960189021e-06
relative error = 7.311938034329691e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.14
Order of pole (six term test) = 9.555
TOP MAIN SOLVE Loop
x[1] = 1.099900000000033
y[1] (analytic) = 1.854669336557465
y[1] (numeric) = 1.854667886158115
absolute error = 1.450399349955944e-06
relative error = 7.820258422172953e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.138
Order of pole (six term test) = 9.53
TOP MAIN SOLVE Loop
x[1] = 1.089900000000034
y[1] (analytic) = 1.848789102956494
y[1] (numeric) = 1.84878755919568
absolute error = 1.543760813849104e-06
relative error = 8.350118525581942e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.136
Order of pole (six term test) = 9.505
TOP MAIN SOLVE Loop
x[1] = 1.079900000000035
y[1] (analytic) = 1.842814263486175
y[1] (numeric) = 1.842812623026019
absolute error = 1.640460155938328e-06
relative error = 8.901928905384963e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.134
Order of pole (six term test) = 9.479
TOP MAIN SOLVE Loop
x[1] = 1.069900000000036
y[1] (analytic) = 1.836746451567484
y[1] (numeric) = 1.836744711048726
absolute error = 1.740518758008847e-06
relative error = 9.476097022120193e-05 %
Correct digits = 7
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.132
Order of pole (six term test) = 9.452
TOP MAIN SOLVE Loop
x[1] = 1.059900000000037
y[1] (analytic) = 1.830587317667437
y[1] (numeric) = 1.830585473711859
absolute error = 1.843955577784939e-06
relative error = 0.0001007302716449787 %
Correct digits = 6
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.131
Order of pole (six term test) = 9.426
TOP MAIN SOLVE Loop
x[1] = 1.049900000000038
y[1] (analytic) = 1.824338528450885
y[1] (numeric) = 1.824336577663735
absolute error = 1.950787150262201e-06
relative error = 0.0001069312038220608 %
Correct digits = 6
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.129
Order of pole (six term test) = 9.4
TOP MAIN SOLVE Loop
x[1] = 1.03990000000004
y[1] (analytic) = 1.818001765930091
y[1] (numeric) = 1.817999704902501
absolute error = 2.061027589705944e-06
relative error = 0.0001133677440985059 %
Correct digits = 6
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.127
Order of pole (six term test) = 9.373
TOP MAIN SOLVE Loop
x[1] = 1.029900000000041
y[1] (analytic) = 1.811578726612742
y[1] (numeric) = 1.811576551924154
absolute error = 2.174688588540974e-06
relative error = 0.0001200438356111174 %
Correct digits = 6
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.125
Order of pole (six term test) = 9.347
TOP MAIN SOLVE Loop
x[1] = 1.019900000000042
y[1] (analytic) = 1.80507112064908
y[1] (numeric) = 1.805068828869648
absolute error = 2.291779432006535e-06
relative error = 0.0001269633869707273 %
Correct digits = 6
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.124
Order of pole (six term test) = 9.322
TOP MAIN SOLVE Loop
x[1] = 1.009900000000043
y[1] (analytic) = 1.798480670978793
y[1] (numeric) = 1.798478258671789
absolute error = 2.41230700392947e-06
relative error = 0.0001341302713371177 %
Correct digits = 6
h = -0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.122
Order of pole (six term test) = 9.297
Finished!
diff ( y , x , 1 ) = expt ( 2.0 , sin ( x ) ) * cos ( x ) * ln ( 2.0 ) ;
Iterations = 4001
Total Elapsed Time = 0.0 Seconds
Elapsed Time(since restart) = 0.0 Seconds
Expected Time Remaining = 0.0 Seconds
Optimized Time Remaining = 0.0 Seconds
Expected Total Time = 0.0 Seconds
Time to Timeout = 30 Minutes 0.0 Seconds
Percent Done = 0 %