Solution Methods for Linear Finite Difference Equations

2 SOLUTION METHODS FOR LINEAR FINITE DIFFERENCE EQUATIONS 

It was stated at the outset that analytical methods for linear difference equations are quite similar to those applied to linear ODE. Thus, we first find the complementary solution to the homogeneous (unforced) equation, and then add the particular solution to this. We shall use the methods of Undetermined Coefficients and Inverse Operators to find particular solutions. 

The general linear finite difference equation of kth order can be written just as we did in Section 2.5 for ODE 

It frequently occurs that the coefficients ai are independent of n and take constant values. Moreover, as we have seen, the second order equation arises most frequently, so we illustrate the complementary solution for this case 

Staged processes usually yield a negative value for Uj, and by comparing with the extraction battery, Eq. 5.7, we require a, = —(/8 + 1) and Uq = /8. 

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Solution Methods for Linear Finite Difference Equations 167 5.2.1 Complementary Solutions... 

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