##############ECHO OF PROBLEM#################
##############temp/mtest7postode.ode#################
diff ( y2 , x , 5 ) = y1 ;
diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 4 ) ;
!
/* BEGIN FIRST INPUT BLOCK */
Digits=32;
max_terms=30;
!
/* END FIRST INPUT BLOCK */
/* BEGIN SECOND INPUT BLOCK */
x_start=0.1;
x_end=0.5;
/* # */
/* # Trouble about Pi/4??? */
/* # */
array_y1_init[0 + 1] = exact_soln_y1(x_start);
array_y2_init[0 + 1] = exact_soln_y2(x_start);
array_y2_init[1 + 1] = exact_soln_y2p(x_start);
array_y2_init[2 + 1] = exact_soln_y2pp(x_start);
array_y2_init[3 + 1] = exact_soln_y2ppp(x_start);
array_y2_init[4 + 1] = exact_soln_y2pppp(x_start);
glob_look_poles=true;
glob_max_iter=200000;
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 */
double exact_soln_y1 (double x) {
return( cos(x) );
}
double exact_soln_y2 (double x) {
return( sin(x) + 10.0 * x + 10.0);
}
double exact_soln_y2p (double x) {
return( cos(x) + 10.0);
}
double exact_soln_y2pp (double x) {
return( -sin(x));
}
double exact_soln_y2ppp (double x) {
return( -cos(x));
}
double exact_soln_y2pppp (double x) {
return( sin(x));
}
/* 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 = 0.4
estimated_steps = 400000.0000000001
step_error = 2.5e-16
est_needed_step_err = 2.5e-16
opt_iter = 1
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.467208610116497e-183
estimated_step_error = 2.467208610116497e-183
best_h = 2e-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 = 1.65571567075937e-175
estimated_step_error = 1.65571567075937e-175
best_h = 4e-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 = 1.111131977716593e-167
estimated_step_error = 1.111131977716593e-167
best_h = 8e-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 = 7.45668047786339e-160
estimated_step_error = 7.45668047786339e-160
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 = 5.004093560803892e-152
estimated_step_error = 5.004093560803892e-152
best_h = 3.2e-05
opt_iter = 6
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.358190342152641e-144
estimated_step_error = 3.358190342152641e-144
best_h = 6.4e-05
opt_iter = 7
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.253643389576351e-136
estimated_step_error = 2.253643389576351e-136
best_h = 0.000128
opt_iter = 8
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.512394477355783e-128
estimated_step_error = 1.512394477355783e-128
best_h = 0.0001
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y2[1] (analytic) = 11.09983341664683
y2[1] (numeric) = 11.09983341664683
absolute error = 0
relative error = 0 %
Correct digits = 16
h = 0.0001
y1[1] (analytic) = 0.9950041652780258
y1[1] (numeric) = 0.9950041652780258
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
Radius of convergence (three term test) for eq 1 = 0.09933
Order of pole (three term test) = 22.99
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.09933
Order of pole (three term test) = 22.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.1100000000000003
y2[1] (analytic) = 11.20977830083718
y2[1] (numeric) = 11.20977830083718
absolute error = 0
relative error = 0 %
Correct digits = 16
h = 0.0001
y1[1] (analytic) = 0.9939560979566968
y1[1] (numeric) = 0.9939560979566964
absolute error = 4.440892098500626e-16
relative error = 4.467895621979574e-14 %
Correct digits = 16
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1091
Order of pole (three term test) = 22.99
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1091
Order of pole (three term test) = 22.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.1200000000000006
y2[1] (analytic) = 11.31971220728893
y2[1] (numeric) = 11.31971220728892
absolute error = 1.06581410364015e-14
relative error = 9.415558312108475e-14 %
Correct digits = 16
h = 0.0001
y1[1] (analytic) = 0.9928086358538661
y1[1] (numeric) = 0.9928086358538654
absolute error = 7.771561172376096e-16
relative error = 7.827854121849127e-14 %
Correct digits = 16
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1189
Order of pole (three term test) = 22.99
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1189
Order of pole (three term test) = 22.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.1300000000000002
y2[1] (analytic) = 11.4296341426197
y2[1] (numeric) = 11.4296341426197
absolute error = 1.77635683940025e-15
relative error = 1.554167716336986e-14 %
Correct digits = 16
h = 0.0001
y1[1] (analytic) = 0.991561893714788
y1[1] (numeric) = 0.9915618937147874
absolute error = 5.551115123125783e-16
relative error = 5.598354634554463e-14 %
Correct digits = 16
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1285
Order of pole (three term test) = 22.98
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1285
Order of pole (three term test) = 22.02
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.1400999999999991
y2[1] (analytic) = 11.54064213554597
y2[1] (numeric) = 11.54064213554598
absolute error = 8.881784197001252e-15
relative error = 7.696091857527364e-14 %
Correct digits = 16
h = 0.0001
y1[1] (analytic) = 0.9902020369501161
y1[1] (numeric) = 0.9902020369501152
absolute error = 8.881784197001252e-16
relative error = 8.969668679290643e-14 %
Correct digits = 16
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1383
Order of pole (three term test) = 22.98
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1383
Order of pole (three term test) = 22.02
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.150099999999998
y2[1] (analytic) = 11.65053700883401
y2[1] (numeric) = 11.65053700883403
absolute error = 1.598721155460225e-14
relative error = 1.372229584136762e-13 %
Correct digits = 15
h = 0.0001
y1[1] (analytic) = 0.9887561291789647
y1[1] (numeric) = 0.9887561291789638
absolute error = 8.881784197001252e-16
relative error = 8.982785476512228e-14 %
Correct digits = 16
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1479
Order of pole (three term test) = 22.98
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1479
Order of pole (three term test) = 22.02
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.1600999999999969
y2[1] (analytic) = 11.76041692854579
y2[1] (numeric) = 11.76041692854583
absolute error = 3.375077994860476e-14
relative error = 2.869862535798561e-13 %
Correct digits = 15
h = 0.0001
y1[1] (analytic) = 0.9872113466188561
y1[1] (numeric) = 0.9872113466188553
absolute error = 7.771561172376096e-16
relative error = 7.872236476002084e-14 %
Correct digits = 16
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1574
Order of pole (three term test) = 22.97
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1574
Order of pole (three term test) = 22.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.1700999999999958
y2[1] (analytic) = 11.87028090669756
y2[1] (numeric) = 11.87028090669761
absolute error = 4.440892098500626e-14
relative error = 3.74118534633409e-13 %
Correct digits = 15
h = 0.0001
y1[1] (analytic) = 0.9855678437467591
y1[1] (numeric) = 0.9855678437467585
absolute error = 5.551115123125783e-16
relative error = 5.632402841008414e-14 %
Correct digits = 16
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1668
Order of pole (three term test) = 22.97
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1668
Order of pole (three term test) = 22.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.1800999999999947
y2[1] (analytic) = 11.98012795689973
y2[1] (numeric) = 11.98012795689979
absolute error = 6.217248937900877e-14
relative error = 5.189634835511225e-13 %
Correct digits = 15
h = 0.0001
y1[1] (analytic) = 0.9838257849115911
y1[1] (numeric) = 0.9838257849115905
absolute error = 6.661338147750939e-16
relative error = 6.770851353880243e-14 %
Correct digits = 16
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1762
Order of pole (three term test) = 22.97
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1762
Order of pole (three term test) = 22.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.1900999999999936
y2[1] (analytic) = 12.08995709445548
y2[1] (numeric) = 12.08995709445555
absolute error = 6.927791673660977e-14
relative error = 5.730203688512755e-13 %
Correct digits = 15
h = 0.0001
y1[1] (analytic) = 0.9819853443177842
y1[1] (numeric) = 0.9819853443177832
absolute error = 9.992007221626409e-16
relative error = 1.01753119631008e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1856
Order of pole (three term test) = 22.96
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1856
Order of pole (three term test) = 22.04
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.2000999999999925
y2[1] (analytic) = 12.19976733645925
y2[1] (numeric) = 12.19976733645934
absolute error = 8.526512829121202e-14
relative error = 6.989078229090112e-13 %
Correct digits = 15
h = 0.0001
y1[1] (analytic) = 0.9800467060078638
y1[1] (numeric) = 0.9800467060078623
absolute error = 1.554312234475219e-15
relative error = 1.585957306878339e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1948
Order of pole (three term test) = 22.96
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1948
Order of pole (three term test) = 22.04
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.2100999999999913
y2[1] (analytic) = 12.30955770189501
y2[1] (numeric) = 12.30955770189511
absolute error = 9.947598300641403e-14
relative error = 8.081198806282052e-13 %
Correct digits = 15
h = 0.0001
y1[1] (analytic) = 0.9780100638440457
y1[1] (numeric) = 0.9780100638440441
absolute error = 1.554312234475219e-15
relative error = 1.589259959520285e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.204
Order of pole (three term test) = 22.96
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.204
Order of pole (three term test) = 22.04
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.2200999999999902
y2[1] (analytic) = 12.41932721173438
y2[1] (numeric) = 12.4193272117345
absolute error = 1.154631945610163e-13
relative error = 9.29705712656649e-13 %
Correct digits = 15
h = 0.0001
y1[1] (analytic) = 0.9758756214888487
y1[1] (numeric) = 0.9758756214888464
absolute error = 2.220446049250313e-15
relative error = 2.275337143746537e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2131
Order of pole (three term test) = 22.95
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2131
Order of pole (three term test) = 22.05
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.2300999999999891
y2[1] (analytic) = 12.52907488903452
y2[1] (numeric) = 12.52907488903464
absolute error = 1.190159082398168e-13
relative error = 9.499177656283292e-13 %
Correct digits = 15
h = 0.0001
y1[1] (analytic) = 0.9736435923847299
y1[1] (numeric) = 0.9736435923847273
absolute error = 2.55351295663786e-15
relative error = 2.622636226037888e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2221
Order of pole (three term test) = 22.95
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2221
Order of pole (three term test) = 22.05
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.240099999999988
y2[1] (analytic) = 12.63879975903581
y2[1] (numeric) = 12.63879975903595
absolute error = 1.403321903126198e-13
relative error = 1.110328456721475e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9713141997327395
y1[1] (numeric) = 0.9713141997327365
absolute error = 2.997602166487923e-15
relative error = 3.086130283396169e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.231
Order of pole (three term test) = 22.94
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.231
Order of pole (three term test) = 22.06
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.2500999999999869
y2[1] (analytic) = 12.74850084925937
y2[1] (numeric) = 12.74850084925952
absolute error = 1.49213974509621e-13
relative error = 1.170443303679034e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9688876764702017
y1[1] (numeric) = 0.9688876764701982
absolute error = 3.441691376337985e-15
relative error = 3.552208847238687e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2398
Order of pole (three term test) = 22.94
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2398
Order of pole (three term test) = 22.06
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.2600999999999858
y2[1] (analytic) = 12.85817718960425
y2[1] (numeric) = 12.85817718960442
absolute error = 1.70530256582424e-13
relative error = 1.326239746643845e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9663642652474206
y1[1] (numeric) = 0.966364265247417
absolute error = 3.552713678800501e-15
relative error = 3.676371122736923e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2485
Order of pole (three term test) = 22.93
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2485
Order of pole (three term test) = 22.07
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.2700999999999847
y2[1] (analytic) = 12.96782781244448
y2[1] (numeric) = 12.96782781244466
absolute error = 1.740829702612245e-13
relative error = 1.342421975206727e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9637442184034157
y1[1] (numeric) = 0.9637442184034118
absolute error = 3.885780586188048e-15
relative error = 4.031962539422977e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2572
Order of pole (three term test) = 22.93
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2572
Order of pole (three term test) = 22.07
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.2800999999999836
y2[1] (analytic) = 13.07745175272583
y2[1] (numeric) = 13.07745175272601
absolute error = 1.811883976188255e-13
relative error = 1.385502321437043e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9610277979406879
y1[1] (numeric) = 0.9610277979406836
absolute error = 4.329869796038111e-15
relative error = 4.505457391884245e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2657
Order of pole (three term test) = 22.92
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2657
Order of pole (three term test) = 22.08
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.2900999999999825
y2[1] (analytic) = 13.18704804806227
y2[1] (numeric) = 13.18704804806246
absolute error = 1.865174681370263e-13
relative error = 1.414398942486855e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.95821527549902
y1[1] (numeric) = 0.9582152754990146
absolute error = 5.329070518200751e-15
relative error = 5.561454356303675e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2741
Order of pole (three term test) = 22.92
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2741
Order of pole (three term test) = 22.08
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.3000999999999814
y2[1] (analytic) = 13.29661573883229
y2[1] (numeric) = 13.29661573883249
absolute error = 2.060573933704291e-13
relative error = 1.549698039093104e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9553069323283122
y1[1] (numeric) = 0.9553069323283064
absolute error = 5.773159728050814e-15
relative error = 6.043251161153242e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2824
Order of pole (three term test) = 22.91
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2824
Order of pole (three term test) = 22.09
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.3100999999999803
y2[1] (analytic) = 13.40615386827476
y2[1] (numeric) = 13.40615386827499
absolute error = 2.220446049250313e-13
relative error = 1.65628865002432e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9523030592604581
y1[1] (numeric) = 0.9523030592604516
absolute error = 6.550315845288424e-15
relative error = 6.878394206120985e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2906
Order of pole (three term test) = 22.91
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2906
Order of pole (three term test) = 22.09
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.3200999999999792
y2[1] (analytic) = 13.51566148258471
y2[1] (numeric) = 13.51566148258494
absolute error = 2.344791028008331e-13
relative error = 1.734869603703568e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9492039566802611
y1[1] (numeric) = 0.9492039566802544
absolute error = 6.772360450213455e-15
relative error = 7.134778993019644e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2987
Order of pole (three term test) = 22.9
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2987
Order of pole (three term test) = 22.1
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.3300999999999781
y2[1] (analytic) = 13.62513763100861
y2[1] (numeric) = 13.62513763100885
absolute error = 2.415845301584341e-13
relative error = 1.773079558540581e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9460099344953968
y1[1] (numeric) = 0.9460099344953896
absolute error = 7.216449660063518e-15
relative error = 7.628302195275341e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3066
Order of pole (three term test) = 22.89
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3066
Order of pole (three term test) = 22.11
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.340099999999977
y2[1] (analytic) = 13.73458136593952
y2[1] (numeric) = 13.73458136593978
absolute error = 2.575717417130363e-13
relative error = 1.875351966327784e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9427213121054221
y1[1] (numeric) = 0.9427213121054143
absolute error = 7.771561172376096e-15
relative error = 8.243752498837135e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3145
Order of pole (three term test) = 22.89
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3145
Order of pole (three term test) = 22.11
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.3500999999999759
y2[1] (analytic) = 13.84399174301183
y2[1] (numeric) = 13.84399174301209
absolute error = 2.629008122312371e-13
relative error = 1.899024624627822e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9393384183698352
y1[1] (numeric) = 0.9393384183698268
absolute error = 8.43769498715119e-15
relative error = 8.982593304119613e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3222
Order of pole (three term test) = 22.88
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3222
Order of pole (three term test) = 22.12
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.3600999999999748
y2[1] (analytic) = 13.95336782119566
y2[1] (numeric) = 13.95336782119594
absolute error = 2.824407374646398e-13
relative error = 2.024176106327552e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9358615915751908
y1[1] (numeric) = 0.9358615915751819
absolute error = 8.881784197001252e-15
relative error = 9.490489060515799e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3298
Order of pole (three term test) = 22.88
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3298
Order of pole (three term test) = 22.12
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.3700999999999737
y2[1] (analytic) = 14.062708662891
y2[1] (numeric) = 14.0627086628913
absolute error = 2.948752353404416e-13
relative error = 2.096859448696147e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9322911794012709
y1[1] (numeric) = 0.9322911794012618
absolute error = 9.103828801926284e-15
relative error = 9.765005829801883e-13 %
Correct digits = 15
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3372
Order of pole (three term test) = 22.87
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3372
Order of pole (three term test) = 22.13
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.3800999999999726
y2[1] (analytic) = 14.17201333402148
y2[1] (numeric) = 14.17201333402178
absolute error = 2.984279490192421e-13
relative error = 2.105755491372795e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9286275388863178
y1[1] (numeric) = 0.9286275388863074
absolute error = 1.032507412901396e-14
relative error = 1.111863874013104e-12 %
Correct digits = 14
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3445
Order of pole (three term test) = 22.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3445
Order of pole (three term test) = 22.14
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.3900999999999715
y2[1] (analytic) = 14.28128090412774
y2[1] (numeric) = 14.28128090412804
absolute error = 3.037570195374428e-13
relative error = 2.126959210287975e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9248710363913296
y1[1] (numeric) = 0.9248710363913184
absolute error = 1.121325254871408e-14
relative error = 1.212412553480543e-12 %
Correct digits = 14
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3517
Order of pole (three term test) = 22.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3517
Order of pole (three term test) = 22.14
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.4000999999999704
y2[1] (analytic) = 14.39051044646048
y2[1] (numeric) = 14.3905104464608
absolute error = 3.197442310920451e-13
relative error = 2.221910280956643e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9210220475634256
y1[1] (numeric) = 0.9210220475634139
absolute error = 1.176836406102666e-14
relative error = 1.277750526402707e-12 %
Correct digits = 14
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3587
Order of pole (three term test) = 22.85
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3587
Order of pole (three term test) = 22.15
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.4100999999999693
y2[1] (analytic) = 14.49970103807317
y2[1] (numeric) = 14.49970103807351
absolute error = 3.428368700042483e-13
relative error = 2.364440957120638e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9170809572982812
y1[1] (numeric) = 0.917080957298269
absolute error = 1.221245327087672e-14
relative error = 1.331665778652147e-12 %
Correct digits = 14
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3656
Order of pole (three term test) = 22.84
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3656
Order of pole (three term test) = 22.16
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.4200999999999682
y2[1] (analytic) = 14.6088517599143
y2[1] (numeric) = 14.60885175991466
absolute error = 3.570477247194503e-13
relative error = 2.444050570073995e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9130481597016386
y1[1] (numeric) = 0.9130481597016253
absolute error = 1.321165399303936e-14
relative error = 1.446983256322055e-12 %
Correct digits = 14
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3724
Order of pole (three term test) = 22.83
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3724
Order of pole (three term test) = 22.17
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.4300999999999671
y2[1] (analytic) = 14.71796169691931
y2[1] (numeric) = 14.71796169691968
absolute error = 3.677058657558518e-13
relative error = 2.498347755809271e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9089240580498966
y1[1] (numeric) = 0.9089240580498827
absolute error = 1.387778780781446e-14
relative error = 1.526836888616344e-12 %
Correct digits = 14
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.379
Order of pole (three term test) = 22.83
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.379
Order of pole (three term test) = 22.17
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.440099999999966
y2[1] (analytic) = 14.8270299381021
y2[1] (numeric) = 14.82702993810249
absolute error = 3.854694341498544e-13
relative error = 2.599775111799601e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.904709064749784
y1[1] (numeric) = 0.9047090647497693
absolute error = 1.465494392505207e-14
relative error = 1.619851562900522e-12 %
Correct digits = 14
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3854
Order of pole (three term test) = 22.82
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3854
Order of pole (three term test) = 22.18
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.4500999999999649
y2[1] (analytic) = 14.9360555766461
y2[1] (numeric) = 14.93605557664651
absolute error = 4.050093593832571e-13
relative error = 2.711621935958289e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.9004036012971181
y1[1] (numeric) = 0.900403601297103
absolute error = 1.509903313490213e-14
relative error = 1.676918341191719e-12 %
Correct digits = 14
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3917
Order of pole (three term test) = 22.81
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3917
Order of pole (three term test) = 22.19
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.4600999999999638
y2[1] (analytic) = 15.04503770999499
y2[1] (numeric) = 15.0450377099954
absolute error = 4.103384299014579e-13
relative error = 2.727400474568797e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.8960080982346562
y1[1] (numeric) = 0.89600809823464
absolute error = 1.620925615952729e-14
relative error = 1.809052417211773e-12 %
Correct digits = 14
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3979
Order of pole (three term test) = 22.8
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3979
Order of pole (three term test) = 22.2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.4700999999999627
y2[1] (analytic) = 15.1539754399429
y2[1] (numeric) = 15.15397543994333
absolute error = 4.263256414560601e-13
relative error = 2.81329241389919e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.891522995109042
y1[1] (numeric) = 0.8915229951090253
absolute error = 1.665334536937735e-14
relative error = 1.86796588094068e-12 %
Correct digits = 14
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4038
Order of pole (three term test) = 22.79
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4038
Order of pole (three term test) = 22.21
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.4800999999999616
y2[1] (analytic) = 15.2628678727243
y2[1] (numeric) = 15.26286787272474
absolute error = 4.405364961712621e-13
relative error = 2.886328440007847e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.8869487404268501
y1[1] (numeric) = 0.8869487404268325
absolute error = 1.765254609153999e-14
relative error = 1.990255500339803e-12 %
Correct digits = 14
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4097
Order of pole (three term test) = 22.79
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4097
Order of pole (three term test) = 22.21
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.4900999999999605
y2[1] (analytic) = 15.37171411910331
y2[1] (numeric) = 15.37171411910376
absolute error = 4.494182803682634e-13
relative error = 2.923670560654946e-12 %
Correct digits = 14
h = 0.0001
y1[1] (analytic) = 0.8822857916097371
y1[1] (numeric) = 0.8822857916097188
absolute error = 1.831867990631508e-14
relative error = 2.076275066482995e-12 %
Correct digits = 14
h = 0.0001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4153
Order of pole (three term test) = 22.78
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4153
Order of pole (three term test) = 22.22
NO COMPLEX POLE (six term test) for Equation 2
Finished!
diff ( y2 , x , 5 ) = y1 ;
diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 4 ) ;
Iterations = 4001
Total Elapsed Time = 2.0 Seconds
Elapsed Time(since restart) = 2.0 Seconds
Time to Timeout = 29 Minutes 58.0 Seconds
Percent Done = 100 %