Mathematica codes

The solution method, the Adomian Decomposition Method (ADM), is mechanized for solving the nonlinear models according to the principle of Parameter Decomposition .2,3 A Mathematica code of the ADM,12 for general order reactions in planar or spherical catalyst pellets, is given in more detail in the Appendix. Thus, the algebraic expressions of the approximate solutions and the computed data of results can all be easily obtained. 

For this three-dimensional electrode model, with or without decoupling of the two coupled equations, the approximate solutions can be obtained by using the Mathematica codes of the ADM given in the Appendix.17 The algebraic expressions of dimensionless potential and concentration are in a series form with even orders as... 

PAMC (Parameterized ADM Mathematica Code) for diffusion-reaction models ... 

The two-coupled ordinary differential equations have been decomposed by parameterized ADM, and the Mathematica code is listed below. 

Figure 1.1 shows the isotherms obtained from the MATHEMATICA code below. 

With B = 0.2 and Eq = 30.0, Figure 12.3 shows the (X,S) space where multiple steady states occur. Only the upper and lower values of X are stable, while intermediate values are unstable. It would be interesting to know when the system will jump from one branch to another. This stability problem may be controlled by the direction and magnitude of fluctuations. Figure 12.3 is obtained from the following MATHEMATICA code... 

Figure 13.12 displays the trajectories of X and K and the state—space plot produced by the following MATHEMATICA code ... 

In [182] the authors presented an algorithm and a MATHEMATICA code for the conversion of formulae expressed in terms of the trigonometric functions sin(wx), cos(wx) or hyperbolic functions sinh(ct)x), cosh(ct)x) to formulae expressed in terms of functions. 

Sample Mathematica codes for doing numerical and algebraic calculations using the van der Waals equation are provided in Appendix 1.2. 

CODE A MATHEMATICA CODE FOR EVALUATING THE VAN DER WAALS PRESSURE... 

CODE B MATHEMATICA CODE FOR OBTAINING THE CRITICAL CONSTANTS FOR THE VAN DER WAALS EQUATION... 

CODE C MATHEMATICA CODE FOR OBTAINING THE LAW OF CORRESPONDING STATES... 

Using Table 1.1 and the relations (1.4.4) obtain the critical temperature Tc, critical pressure Pc and critical molar volume for CO2, H2 and CH4. Write a Maple or Mathematica code to calculate the van der Waals constants a and b given Tg, Pc and Vmc for any gas. 

In this equation the initial concentrations [X]o and [Y]q appear explicitly and (0) = 0 for all initial concentrations. The solutions of such equations, (t), can be used to obtain the entropy production, as will be shown explicitly in section 9.5. Differential equations such as these, and more complicated systems, can be numerically solved on a computer, using software such as Mathematica or Maple. Sample Mathematica codes are provided in Appendix 9.1. 

CODE A MATHEMATICA CODE FOR LINEAR KINETICS X (PRODUCTS)... 

CODE C MATHEMATICA CODE FOR RACEMIZATION REACTION L D AND CONSEQUENT ENTROPY PRODUCTION... 

Linear stability analysis does not provide a means of determining how the system will evolve when a state becomes unstable. To understand the system s behavior fully, the full nonlinear equation has to be considered. Often we encounter nonlinear equations for which solutions cannot be obtained analytically. However, with the availability of powerfiil desktop computers and software, numerical solutions can be obtained without much difficulty. To obtain numerical solutions to nonlinear equations considered in the following chapter, Mathematica codes are provided at the end of Chapter 19. 

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