# Accession Number:

## AD0411770

# Title:

## ON THE NUMERICAL SOLUTION OF LINEAR DIFFERENCE EQUATIONS WITH AXILIARY CONDITIONS AT BOTH ENDS,

# Descriptive Note:

# Corporate Author:

## WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1963-05-01

# Pagination or Media Count:

## 20.0

# Abstract:

Methods are presented for the numerical solution of linear difference equations, when the solution is rendered unique, not by the specification of a full set of starting values at one end of the solution sequence, but by the imposition of linear auxiliary conditions on the terms of the sequence near both ends. The cases of constant coefficients and variable coefficients are treated separately. In the former case, the roots of the auxiliary polynomial are not used, and advantage is taken of the fact that, once a particular solution of the homogeneous equation is available, additional linearly independent solutions can be obtained by merely replacing the argument x by x 1, x 2, etc. In the latter case, the initial auxiliary conditions are used to reduce the number of linearly inde pendent solutions of the homogeneous equation in terms of which the desired solution is expressed. Numerical examples are given. Author