Dependence of the unique solution of a periodic boundary value problem on the parameter

Hamid Bellout, Qingkai Kong, Min Wang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this paper, we study the dependence of the unique positive solution of the periodic boundary value problem-u″+ρ2u=w(t)u s,0<s<1andρ≠0,u(0)=u(1),u′(0)=u′(1)on the parameter ρ as ρ → 0. We show that this solution u(t; ρ) is infinitely differentiable in ρ and has singularity in the order of ρ with α = 2/(1 - s) as ρ → 0. Furthermore, the graph of u(t; ρ) has fluctuation in t only of the order O(ρ-α+2). This will help us to determine the location of the solution in numerical computations to study the behavior of the solution when ρ is sufficiently close to 0.

Original languageEnglish (US)
Pages (from-to)7838-7844
Number of pages7
JournalApplied Mathematics and Computation
Volume217
Issue number19
DOIs
StatePublished - Jun 1 2011

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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