Nonlinear Equation Solution
| Variable | Value | f(x) | Initial value | Initial f(x) | |
|---|---|---|---|---|---|
| 1 | Tbp | 95.585087 | 1.6e-12 | 119.6 | 8.1e+2 |
| 2 | xA | 0.6 | 0.6 | ||
| 3 | PA | 1196.2189 | 2227 | ||
| 4 | PB | 485.67158 | 973.7 | ||
| 5 | xB | 0.4 | 0.4 | ||
| 6 | yA | 0.78698615 | 1.465 | ||
| 7 | yB | 0.21301385 | 0.4271 |
Root Finding Plot
Settings and Hints
| Name/Source | Value | Type | |
|---|---|---|---|
| 1 | Number of equations | 7 | Setting |
| 2 | Implicit equations | 1 | Setting |
| 3 | Explicit equations | 6 | Setting |
| 4 | Elapsed time | 0.000 ms | Setting |
| 5 | Solution method | Brent | Setting |
| 6 | Tolerance F | 1e-7 | Setting |
| 7 | Max iterations | 150 | Setting |
| 8 | #@chart_size = 428,300 | Default (array) | |
| 9 | #@report_fix_digits = 8 | Default (integer) | |
| 10 | #@report_show_source = true | Default (boolean) | |
| 11 | #@report_show_header = false | Default (boolean) | |
| 12 | #@report_show_charts = true | Default (boolean) | |
| 13 | #@report_show_settings = true | Default (boolean) | |
Messages
| Severity | Description | |
|---|---|---|
| 1 | Info | -Infor- Implicit variables (1) Tbp |
| 2 | Info | -Infor- Explicit variables (6) xA, PA, PB, xB, yA, yB |
| 3 | Info | -Infor- All variables (7) xA, PA, xB, PB, Tbp, yA, yB |
Source
# Example 26(a) - Solution of DAE system
# Initial Bubble Point.
# Verified Solution: Tbp = 95.5851
# Ref.: Comput. Appl. Eng. Educ. 6: 176, 1998
f(Tbp)=xA*PA+xB*PB-760*1.2
xA=0.6
PA=10^(6.90565-1211.033/(Tbp+220.79))
PB=10^(6.95464-1344.8/(219.482+Tbp))
xB=1-xA
yA=xA*PA/(760*1.2)
yB=xB*PB/(760*1.2)
Tbp(min)=60
Tbp(max)=120
# Initial Bubble Point.
# Verified Solution: Tbp = 95.5851
# Ref.: Comput. Appl. Eng. Educ. 6: 176, 1998
f(Tbp)=xA*PA+xB*PB-760*1.2
xA=0.6
PA=10^(6.90565-1211.033/(Tbp+220.79))
PB=10^(6.95464-1344.8/(219.482+Tbp))
xB=1-xA
yA=xA*PA/(760*1.2)
yB=xB*PB/(760*1.2)
Tbp(min)=60
Tbp(max)=120