Numerical Library Problems Involving Simultaneous Nonlinear Equations
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Legend for following Table |
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1L- Lower, A - Average, H - Higher Difficulty
Levels |
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2S - Function/Variable Scaling Related
Difficulties Exist |
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3DB - Discontinuity/Function Undefined on the
Boundary or DI - Inside the Feasible Subspace |
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4MI - Multiple Solutions Inside or MO - Some
Outside of the Feasible Subspace |
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5F - False Solution/s Exist |
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Problem Characteristics/Difficulties |
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No. |
File Name - Problem Title |
Difficulty |
Scaling2 |
Discontinuity3 |
Multiple |
False |
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Level1 |
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Solutions4 |
Solutions5 |
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ONE NONLINEAR EQUATION |
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1 |
Oneeq1
- Chemical equilibrium calculation |
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2 |
Oneeq2a - Bubble Point of a Non-ideal Mixture
-ethanol, n-hexane -Wilson equation |
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3 |
Oneeq2b - Bubble Pt. of a Non-ideal Mixture
-ethanol, n-heptane -Van Laar equation |
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4 |
Oneeq3 - Kinetic problem |
H |
S |
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5 |
Oneeq4 - Azeotropic point calculation |
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6 |
Oneeq5 - Adiabatic flame temperature |
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7 |
Oneeq6a - Gas Volume from Beattie Bridgeman
Equation of State - Original Form |
H |
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DB |
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8 |
Oneeq6b - Gas Volume from Beattie Bridgeman
Equation of State - Revised Form |
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9 |
Oneeq7
- Conversion in a chemical reactor |
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DI |
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10 |
Oneeq8 - Flow in a smooth pipe |
H |
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11 |
Oneeq9 - Pressure drop in a converging diverging
nozzle |
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DI |
MI |
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12 |
Oneeq10 - Batch Distillation at Infinite Reflux |
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DI |
MI |
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13 |
Oneeq11a - Chemical Equilibrium - 1st Formulation |
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DI |
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14 |
Oneeq11b - Chemical Equilibrium - 2nd Formulation |
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DI |
MI |
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15 |
Oneeq12 - Volume from Virial Equation of State |
H |
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DB |
MI |
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16 |
Oneeq13
- Gas Volume from Redlich-Kwong Equation of
State |
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17 |
Oneeq14 - Heat duty of a countercurrent flow heat
exchanger |
H |
S |
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18 |
Oneeq15a - Sinkage depth of sphere in water - 1st
form |
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19 |
Oneeq15b - Sinkage depth of sphere in water - 2nd
form |
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20 |
Oneeq16 - Adiabatic Flame Temperature for Natural
Gas Combustion |
H |
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21 |
Oneeq17 - Global reaction rate in Catalytic
Oxidation of Nitrogen |
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DI |
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22 |
Oneeq18a - Stability of Batch Fluidized Catalytic
Reactor - Correct Formulation |
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MI |
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23 |
Oneeq18b - Stability of Batch Fluidized Catalytic
Reactor - Rounded Numbers |
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24 |
Oneeq19a - Compressibility factor from the RK
equation - three solutions |
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MI |
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25 |
Oneeq19b - Compressibility factor from the RK
equation - one solution |
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26 |
Oneeq20a - Equilibrium conversion in a tubular
reactor - original form |
H |
S |
DB |
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27 |
Oneeq20b - Equilibrium conversion in a tubular
reactor - revised form |
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28 |
Oneeq21a - General Two-fluid Model Equations -
ugs=-0.0295 |
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MI |
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29 |
Oneeq21b - General Two-fluid Model Equations -
ugs=-0.029 |
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