Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4619235 | Journal of Mathematical Analysis and Applications | 2010 | 7 Pages |
Abstract
We consider the following two classes of second order boundary value problems for difference equation:Δ(ri−1Δyi−1)−biyi+λaiyi=0,1⩽i⩽n,y0−τy1=yn+1−δyn=0 with δ,τ∈[0,1]δ,τ∈[0,1] andΔ(ri−1Δyi−1)−biyi+λaiyi=0,1⩽i⩽n,y0=αyn,yn+1=βy1 with α,β∈[0,1]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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jun Ji, Bo Yang,