Chapter 3. The numerical solution of the direct problem of chemical kinetics

from the book Viktor Korobov & Valery Ochkov "Chemical kinetic with Mathcad & Maple"

png - picture, MC11, MC13 è MC14-15 - Mathcad-files of different versions of Matcad for downloading

MCS - on-line Mathcad calculation

***- working

Fig. 3.1.

Kinetic curve calculation for an intermediate in a consecutive second-order reaction using Odesolve function

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MC11

MC13

MC14-15

Mathcad Prime

MCS

Fig. 3.2.

Calculation of the kinetic curves for all components in a multi-step reaction using ODESOLVE function

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MC11

MC13

MC14-15

 

MCS

Fig. 3.3

Choosing an ODESOLVE algorithm in different Mathcad versions

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Fig. 3.4.

Solving a system of "differential—algebraic" equations

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MC14-15

 

MCS

Fig. 3.5.

Solving a boundary-value problem with solver

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MC11

MC13

MC14-15

 

 

Fig. 3.6.

Numerical solution of the direct problem for a consecutive reaction with two intermediates

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MC11

MC13

MC14-15

 

MCS

Fig. 3.7.

Microorganism population and poison amount trends

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MC11

MC13

MC14-15

 

MCS

Fig. 3.8.

Comparison of the results for calculations with fixed step of integration

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MC11

MC13

MC14-15

 

 

Fig. 3.9.

An example of a kinetic scheme described with a stiff set of differential equations

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MC11

MC13

MC14-15

 

MCS

Fig. 3.10.

Numerical solution of the direct kinetic problem using Mathcad tools

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Maple 9

 

Fig. 3.11.

Kinetic curves for reversible reaction participants calculated using numerical calculation results

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Maple 9

 

Fig. 3.12.

Population trends for predators (dashed line) and prey (solid line) in the
Lotka–Volterra model

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MC11

MC13

MC14-15

 

MCS

Fig. 3.13.

Phase portrait of the Lotka—Volterra system with a critical point

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MC11

MC13

MC14-15

 

MCS

Fig. 3.14.

"Predator—prey" model analysis using Maple

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Maple 9

 

Fig. 3.15.

Phase portrait of the Lotka—Volterra system using a directional field

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MC11

MC13

MC14-15

 

MCS

Fig. 3.16.

Phase portrait of the system with "node"−type critical point

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Maple 9

 

Fig. 3.17.

System with a “saddle” critical point

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MC11

MC13

MC14-15

 

 

Fig. 3.18.

Modelling the photosynthesis kinetics

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MC11

MC13

MC14-15

 

MCS

Fig. 3.19.

Possible critical point types and phase portraits versus different Jacobian
matrix eigenvalues

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Fig. 3.20.

Oscillation mode of the population trend in microorganism colony

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MC11

MC13

MC14-15

 

MCS

Fig. 3.21.

Brusselator phase portrait with a limit cycle

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MC11

MC13

MC14-15

 

MCS

Fig. 3.22.

Concentration oscillations in the Belousov–Zhabotinsky reaction

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MC14/15

 

MCS

Fig. 3.23.

One of the direct problem solutions for the oregonator problem

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MC11

MC13

MC14/15

 

MCS

Fig. 3.24.

Solution of the GeCl4 decomposition problem

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MC11

MC13

MC14-15

 

MCS

Fig. 3.25.

Conversion vs. time and temperature for different heating rates

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MC11

MC13

MC14

 

MCS

Fig. 3.26.

Temperature and reagent concentration changes in a periodic adiabatic
reactor

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MC11

MC13

MC14

 

MCS

Fig. 3.27.

Operation dynamics of a periodic nonadiabatic reactor

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MC11

MC13

MC14

 

MCS

Fig. 3.28.

Temperature and concentration trends in a flow adiabatic reactor

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MC11

MC13

MC14

 

MCS

Fig. 3.29.

Computations of possible stationary states and analysis of their
stability

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MC11

MC13

MC14

 

MCS

Fig. 3.30.

Graphical representation of possible stationary states

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MC11

MC13

MC14

 

MCS

Fig. 3.31.

Phase portrait for exothermic reaction in an adiabatic flow reactor

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MC11

MC13

MC14

 

MCS

 

 

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