Difference Equations and Their Solutions

The application of forward, backward, or central finite differences in the solution of differential equations transforms these equations to difference equations of the form 

In addition, difference equations are obtained from the application of material balances on multistage operations, such as distillation and extraction. 

Depending on their origin, difference equations may be linear or nonlinear, homogeneous or nonhomogeneous, with constant or variable coefficients. For the purposes of this book, it will be necessary to discuss only the methods of solution of homogeneous linear difference equations with constant coefficients. 

The order of a difference equation is the difference between the highest and lowest subscript of the dependent variable in the equation, that is, it is the number of finite steps spanned by the equation. The order of Eq. (3.94) is given by 

The process of obtaining is called solving the difference equation. The methods of obtaining such solutions are analogous to those used in finding analytical solutions of differential equations. As a matter of fact, the theory of difference equations is parallel to the corresponding theory of differential equations. Difference equations resemble ordinary 

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