ON THE NUMERICAL SOLUTION OF LINEAR DIFFERENCE EQUATIONS WITH AXILIARY CONDITIONS AT BOTH ENDS,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1963
- Accession Number
- AD0411770
Entities
People
- T.n.e. Greville
Organizations
- University of Wisconsin–Madison