| Variable ▲ | Initial | Minimal | Maximal | Final Value | |
|---|---|---|---|---|---|
| 1 | CA | 0.2 | 0.1404 | 0.2 | 0.14046057 |
| 2 | CA1 | 0.2 | 0.1404 | 0.2 | 0.14044568 |
| 3 | CAanal | 0.2 | 0.1383 | 0.2 | 0.13827264 |
| 4 | derr | 1 | 1 | 1.446 | 1.4464177 |
| 5 | err | -130 | -130 | 2.764 | 2.7643828 |
| 6 | err1 | -130 | -130 | 2.746 | 2.7455795 |
| 7 | y | -130 | -130 | 2.764 | 2.7643828 |
| 8 | y1 | -130 | -130 | 2.746 | 2.7455795 |
| 9 | ynew | -5.227e-11 | -131.9 | -5.227e-11 | -131.9112 |
| 10 | z | 0 | 0 | 0.001 | 0.001 |
Calculated values
Data Table (33 records)
| # | z | CA | y | CA1 | y1 | err | err1 | CAanal | derr | ynew |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 0.2 | -130 | 0.2 | -130.013 | -130 | -130.013 | 0.2 | 1 | -5.2267524e-11 |
| 2 | 0.000006 | 0.199223 | -129.00194 | 0.19922292 | -129.01494 | -129.00194 | -129.01494 | 0.19921152 | 1.000015 | -0.99999 |
| 3 | 0.000031 | 0.19604956 | -124.8847 | 0.19604915 | -124.89771 | -124.8847 | -124.89771 | 0.1959903 | 1.0004004 | -5.165288 |
| 4 | 0.00006433333 | 0.19197686 | -119.49586 | 0.19197603 | -119.50888 | -119.49586 | -119.50888 | 0.19185384 | 1.001725 | -10.709912 |
| 5 | 0.00009766666 | 0.18808194 | -114.21767 | 0.18808065 | -114.23073 | -114.21767 | -114.23073 | 0.18789503 | 1.0039772 | -16.234783 |
| 6 | 0.000131 | 0.18436117 | -109.04525 | 0.18435946 | -109.05835 | -109.04525 | -109.05835 | 0.18411021 | 1.007159 | -21.729847 |
| 7 | 0.00016433334 | 0.18081112 | -103.97381 | 0.18080898 | -103.98695 | -103.97381 | -103.98695 | 0.18049587 | 1.0112734 | -27.185263 |
| 8 | 0.00019766667 | 0.17742851 | -98.99864 | 0.17742592 | -99.01185 | -98.99864 | -99.01185 | 0.17704868 | 1.0163243 | -32.591484 |
| 9 | 0.000231 | 0.17421019 | -94.11514 | 0.17420717 | -94.12843 | -94.11514 | -94.12843 | 0.17376544 | 1.0223162 | -37.939304 |
| 10 | 0.00026433333 | 0.1711532 | -89.3188 | 0.17114973 | -89.332184 | -89.3188 | -89.332184 | 0.17064309 | 1.0292549 | -43.21994 |
| 11 | 0.00029766667 | 0.16825469 | -84.60516 | 0.16825077 | -84.61865 | -84.60516 | -84.61865 | 0.16767877 | 1.0371467 | -48.425068 |
| 12 | 0.000331 | 0.16551198 | -79.96988 | 0.16550761 | -79.983475 | -79.96988 | -79.983475 | 0.16486971 | 1.0459988 | -53.546875 |
| 13 | 0.00036433333 | 0.16292255 | -75.40864 | 0.16291772 | -75.42236 | -75.40864 | -75.42236 | 0.16221333 | 1.0558195 | -58.5781 |
| 14 | 0.00039766668 | 0.16048397 | -70.91723 | 0.16047868 | -70.93109 | -70.91723 | -70.93109 | 0.15970714 | 1.066618 | -63.512062 |
| 15 | 0.000431 | 0.158194 | -66.491486 | 0.15818825 | -66.50551 | -66.491486 | -66.50551 | 0.15734886 | 1.0784041 | -68.3427 |
| 16 | 0.00046433334 | 0.15605052 | -62.127316 | 0.1560443 | -62.141502 | -62.127316 | -62.141502 | 0.15513627 | 1.0911888 | -73.06456 |
| 17 | 0.00049766665 | 0.15405154 | -57.820675 | 0.15404484 | -57.83504 | -57.820675 | -57.83504 | 0.15306735 | 1.1049839 | -77.67284 |
| 18 | 0.000531 | 0.15219522 | -53.567577 | 0.15218803 | -53.582134 | -53.567577 | -53.582134 | 0.15114015 | 1.1198022 | -82.16336 |
| 19 | 0.00056433334 | 0.15047981 | -49.364082 | 0.15047215 | -49.378845 | -49.364082 | -49.378845 | 0.14935292 | 1.1356575 | -86.5326 |
| 20 | 0.00059766666 | 0.14890376 | -45.206295 | 0.1488956 | -45.22128 | -45.206295 | -45.22128 | 0.14770399 | 1.1525644 | -90.77764 |
| 21 | 0.000631 | 0.1474656 | -41.090374 | 0.14745693 | -41.10559 | -41.090374 | -41.10559 | 0.14619184 | 1.1705387 | -94.89619 |
| 22 | 0.00066433335 | 0.14616399 | -37.012497 | 0.1461548 | -37.02796 | -37.012497 | -37.02796 | 0.14481504 | 1.1895967 | -98.88651 |
| 23 | 0.00069766666 | 0.14499772 | -32.9689 | 0.14498802 | -32.984623 | -32.9689 | -32.984623 | 0.14357236 | 1.2097564 | -102.74749 |
| 24 | 0.000731 | 0.14396572 | -28.955826 | 0.1439555 | -28.97183 | -28.955826 | -28.97183 | 0.14246261 | 1.2310362 | -106.47849 |
| 25 | 0.00076433335 | 0.14306703 | -24.969568 | 0.14305627 | -24.985863 | -24.969568 | -24.985863 | 0.1414848 | 1.2534561 | -110.07942 |
| 26 | 0.00079766667 | 0.14230083 | -21.006432 | 0.14228952 | -21.023033 | -21.006432 | -21.023033 | 0.140638 | 1.2770365 | -113.55064 |
| 27 | 0.000831 | 0.14166638 | -17.062746 | 0.14165452 | -17.07967 | -17.062746 | -17.07967 | 0.13992141 | 1.3017997 | -116.89295 |
| 28 | 0.00086433336 | 0.14116313 | -13.134862 | 0.1411507 | -13.152123 | -13.134862 | -13.152123 | 0.13933441 | 1.3277681 | -120.10757 |
| 29 | 0.0008976667 | 0.1407906 | -9.21914 | 0.14077757 | -9.236755 | -9.21914 | -9.236755 | 0.13887642 | 1.3549662 | -123.19604 |
| 30 | 0.000931 | 0.14054842 | -5.3119555 | 0.14053482 | -5.32994 | -5.3119555 | -5.32994 | 0.13854703 | 1.3834189 | -126.16027 |
| 31 | 0.00096433336 | 0.14043641 | -1.4096894 | 0.1404222 | -1.4280604 | -1.4096894 | -1.4280604 | 0.13834594 | 1.4131527 | -129.00246 |
| 32 | 0.0009976666 | 0.14045443 | 2.4912713 | 0.1404396 | 2.4724967 | 2.4912713 | 2.4724967 | 0.13827296 | 1.444195 | -131.72502 |
| 33 | 0.001 | 0.14046057 | 2.7643828 | 0.14044568 | 2.7455795 | 2.7643828 | 2.7455795 | 0.13827264 | 1.4464177 | -131.9112 |
Raw data presented with 33 records.
Constant Values
| Constant | k | DAB | y0 | L | delta |
|---|---|---|---|---|---|
| Value | 0.001 | 1.2e-9 | -130 | 0.001 | 0.0001 |
Settings and Hints
| Name/Source | Value | Type | |
|---|---|---|---|
| 1 | Total number of equations | 14 | Setting |
| 2 | Number of differential equations | 4 | Setting |
| 3 | Number of explicit equations | 10 | Setting |
| 4 | Reporting digits | 10 | Setting |
| 5 | Minimal License | Free - 2 | Setting |
| 6 | Elapsed time | 0.076 ms | Setting |
| 7 | Solution method | RKF_45 | Setting |
| 8 | Step size guess. h | 0.000011666667 | Setting |
| 9 | Truncation error tolerance. eps | 0.000001 | Setting |
| 10 | Good steps | 33 | Setting |
| 11 | Bad steps | 0 | Setting |
| 12 | Calculated Intermediate data points | 50 | Setting |
| 13 | Version | 7.0.73 | Setting |
| 14 | #@chart_size = 428,300 | Default (array2) | |
| 15 | #@chart_interpolate = 2 | Default (integer) | |
| 16 | #@chart_curve_width = 2 | Default (integer) | |
| 17 | #@report_fix_digits = 8 | Default (integer) | |
| 18 | #@report_show_charts = true | Default (boolean) | |
| 19 | #@report_show_data_points = true | Default (boolean) | |
| 20 | #@report_show_intermediate_data_points = true | Default (boolean) | |
| 21 | #@report_show_source = true | Default (boolean) | |
| 22 | #@report_show_header = false | Default (boolean) | |
| 23 | #@report_show_settings = true | Default (boolean) | |
| 24 | #@chart_all_curves = false | Default (boolean) | |
| 25 | #@chart_curves_stiff_grouping_percent = 50 | Default (integer) | |
| 26 | #@chart_y_curves = | Default (array2) | |
| 27 | #@chart_log_scales = 000 | Default (string) | |
Messages
| Severity | Description | |
|---|---|---|
| 1 | Info | -Infor- Differential variables (4) ; CA, y, CA1, y1 |
| 2 | Info | -Infor- Explicit variables (10) ; k, DAB, err, err1, y0, L, delta, CAanal, derr, ynew |
| 3 | Info | -Infor- Independent variable = z |
Source
# Example 25- Boundary Value ODE System
# Diffusion with Reaction
# Verified Final Values: CA = 0.140461, y = 2.76438
# Ref.: Comput. Appl. Eng. Educ. 6: 175-176, 1998
d(CA)/d(z)=y
d(y)/d(z)=k*CA/DAB
d(CA1)/d(z)=y1
d(y1)/d(z)=k*CA1/DAB
k=0.001
DAB=1.2E-9
err=y-0
err1=y1-0
y0=-130
L=.001
delta=0.0001
CAanal=0.2*cosh(L*(k/DAB)^.5*(1-z/L))/(cosh(L*(k/DAB)^.5))
derr=(err1-err)/(delta*y0)
ynew=y0-err/derr
z(0)=0
CA(0)=0.2
y(0)=-130
CA1(0)=0.2
y1(0)=-130.013
z(f)=0.001
# Diffusion with Reaction
# Verified Final Values: CA = 0.140461, y = 2.76438
# Ref.: Comput. Appl. Eng. Educ. 6: 175-176, 1998
d(CA)/d(z)=y
d(y)/d(z)=k*CA/DAB
d(CA1)/d(z)=y1
d(y1)/d(z)=k*CA1/DAB
k=0.001
DAB=1.2E-9
err=y-0
err1=y1-0
y0=-130
L=.001
delta=0.0001
CAanal=0.2*cosh(L*(k/DAB)^.5*(1-z/L))/(cosh(L*(k/DAB)^.5))
derr=(err1-err)/(delta*y0)
ynew=y0-err/derr
z(0)=0
CA(0)=0.2
y(0)=-130
CA1(0)=0.2
y1(0)=-130.013
z(f)=0.001