Numerical Library Problems Involving Simultaneous Nonlinear Equations

 

Legend for following Table

 

 

 

 

 

 

 

1L- Lower, A - Average, H - Higher Difficulty Levels

 

 

 

 

 

 

 

2S - Function/Variable Scaling Related Difficulties Exist

 

 

 

 

 

 

 

3DB - Discontinuity/Function Undefined on the Boundary or DI - Inside the Feasible Subspace

 

 

 

 

 

 

4MI - Multiple Solutions Inside or MO - Some Outside of the Feasible Subspace

 

 

 

 

 

 

 

5F - False Solution/s Exist

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Problem Characteristics/Difficulties

No.

File Name - Problem Title

Difficulty

Scaling2

Discontinuity3

Multiple

False

 

 

 

Level1

 

 

Solutions4

Solutions5

 

 

ONE NONLINEAR EQUATION

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

Oneeq1 - Chemical equilibrium calculation

 

 

 

 

 

 

2

Oneeq2a - Bubble Point of a Non-ideal Mixture -ethanol, n-hexane -Wilson equation

 

 

 

 

 

 

3

Oneeq2b - Bubble Pt. of a Non-ideal Mixture -ethanol, n-heptane -Van Laar equation

 

 

 

 

 

 

4

Oneeq3 - Kinetic problem

H

S

 

 

 

 

5

Oneeq4 - Azeotropic point calculation

 

 

 

 

 

 

6

Oneeq5 - Adiabatic flame temperature

 

 

 

 

 

 

7

Oneeq6a - Gas Volume from Beattie Bridgeman Equation of State - Original Form

H

 

DB

 

 

 

8

Oneeq6b - Gas Volume from Beattie Bridgeman Equation of State - Revised Form

 

 

 

 

 

 

9

Oneeq7 - Conversion in a chemical reactor

 

 

DI

 

 

 

10

Oneeq8 - Flow in a smooth pipe

H

 

 

 

 

 

11

Oneeq9 - Pressure drop in a converging diverging nozzle

 

 

DI

MI

 

 

12

Oneeq10 - Batch Distillation at Infinite Reflux

 

 

DI

MI

 

 

13

Oneeq11a - Chemical Equilibrium - 1st Formulation

 

 

DI

 

 

 

14

Oneeq11b - Chemical Equilibrium - 2nd Formulation

 

 

DI

MI

 

 

15

Oneeq12 - Volume from Virial Equation of State

H

 

DB

MI

 

 

16

Oneeq13 - Gas Volume from Redlich-Kwong Equation of State

 

 

 

 

 

 

17

Oneeq14 - Heat duty of a countercurrent flow heat exchanger

H

S

 

 

 

 

18

Oneeq15a - Sinkage depth of sphere in water - 1st form

 

 

 

 

 

 

19

Oneeq15b - Sinkage depth of sphere in water - 2nd form

 

 

 

 

 

 

20

Oneeq16 - Adiabatic Flame Temperature for Natural Gas Combustion

H

 

 

 

 

 

21

Oneeq17 - Global reaction rate in Catalytic Oxidation of Nitrogen

 

 

DI

 

 

 

22

Oneeq18a - Stability of Batch Fluidized Catalytic Reactor - Correct Formulation

 

 

 

MI

 

 

23

Oneeq18b - Stability of Batch Fluidized Catalytic Reactor - Rounded Numbers

 

 

 

 

 

 

24

Oneeq19a - Compressibility factor from the RK equation - three solutions

 

 

 

MI

 

 

25

Oneeq19b - Compressibility factor from the RK equation - one solution

 

 

 

 

 

 

26

Oneeq20a - Equilibrium conversion in a tubular reactor - original form

H

S

DB

 

 

 

27

Oneeq20b - Equilibrium conversion in a tubular reactor - revised form

 

 

 

 

 

 

28

Oneeq21a - General Two-fluid Model Equations - ugs=-0.0295 

 

 

 

MI

 

 

29

Oneeq21b - General Two-fluid Model Equations - ugs=-0.029