Numerical Solution of Simultaneous Linear Algebraic Equations

Numerical Solution of Simultaneous Linear Algebraic Equations 

In the remainder of this section, we give several examples of systems drawing from chemical engineering applications that yield sets of simultaneous linear algebraic equations. In the following sections of this chapter, we discuss several methods for the numerical solution of such problems and demonstrate the application of these methods on the computer. 

Material and energy balances are the primary tools of chemical engineers. Such balances applied to multistage or multicomponent processes result in sets of equations that can be either differential or algebraic. Often the systems under analysis are nonlinear, thus resulting in sets of nonlinear equations. However, many procedures have been developed that linearize the equations and apply iterative convergence techniques to arrive at the solution of the nonlinear systems. 

A classical example of the use of these techniques is in the analysis of di.stiliation columns, such as the one shown in Fig. 2.1. Steady-state material balances applied to the rectifying section of the column yield the following equations  

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Numerical Solution of Simultaneous Linear Algebraic Equations Chapter 2... 

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