Title

Positive Solutions for Boundary Value Problems of Second Order Difference Equations and Their Computation

Department

Mathematics

Document Type

Article

Publication Date

7-15-2010

Abstract

We consider the following two classes of second order boundary value problems for difference equation: Δ(ri―1Δyi―1) ― biy¡ + λa¡y¡ = 0, 1 ≤ i ≤ n, y0 ― τy1 = yn+1 ― δyn = 0 with δ, τ ∈ [0, 1] and Δ(ri―1Δyi―1) ― biyi + λaiyi = 0, 1 ≤ i ≤ n, y0 = αYn, Yn+1 = βy1 with α, β ∈ [0, 1]. We establish the existence of positive solutions to both problems. A solver with linear computational complexity for almost tridiagonal linear systems is developed by exploring the special structure of linear system of equations. Based on fast solvers for linear systems, effective algorithms for the computation of positive solutions will be proposed.