Computer software Solve Maple Mathematica

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. 

In practice, the solution of polynomial equations is problematic if no simple roots are found by trial and error. In such circumstances the graphical method may be used or, in the cases of a quadratic or cubic equation, there exist algebraic formulae for determining the roots. Alternatively, computer algebra software (such as Maple or Mathematica, for example) can be used to solve such equations... 

Throughout this book, we have seen that when more than one species is involved in a process or when energy balances are required, several balance equations must be derived and solved simultaneously. For steady-state systems the equations are algebraic, but when the systems are transient, simultaneous differential equations must be solved. For the simplest systems, analytical solutions may be obtained by hand, but more commonly numerical solutions are required. Software packages that solve general systems of ordinary differential equations— such as Mathematica , Maple , Matlab , TK-Solver , Polymath , and EZ-Solve —are readily obtained for most computers. Other software packages have been designed specifically to simulate transient chemical processes. Some of these dynamic process simulators run in conjunction with the steady-state flowsheet simulators mentioned in Chapter 10 (e.g.. SPEEDUP, which runs with Aspen Plus, and a dynamic component of HYSYS ) and so have access to physical property databases and thermodynamic correlations. 

A second option is to use existing packages for numerical methods. The software libraries by IMSL and NAG have a wide variety of state-of-the-art numerical integrators. These libraries are well documented, reliable, and flexible, and can be found at most university computing centers or networks. The packages Matlab, Mathematica, and Maple are more interactive and also have programs for solving ordinary differential equations. 

Before closing this section it should be mentioned that most of the methods discussed above can be solved using commercially available programs such as symbolic computation (Mathematica, Maple, or Mathcad 3.0), equation solvers (TK Solver Plus or Mathcad 3.0), spreadsheets (e.g., Lotus 123, Quattro Pro, Microsoft Excel, or Wingz), simulators (Extend or Stella), or Microsoft FORTRAN 5.0. For example, one can introduce the idea of molecular mechanics on model systems using a spreadsheet. Actual applications of molecular mechanics are much better carried out on a software package designed for that purpose, however. 

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