On three theorems of lees for numerical treatment of semilinear two-point boundary value problems

Tetsuro Yamamoto, Shinichi Oishi

    Research output: Contribution to journalArticle

    Abstract

    This paper is concerned with semilinear tow-point boundary value problems of the form -(p(x)u′)′ + f(x, u) = 0, a ≤ x ≤ b, α0u(a) - α1u′(a) = α, β1u′(b) + β,1u′(b) = β, αi ≥ 0, βi≥ 0, i = 0, 1, α01 > 0, β01 > 0, α00 > 0. Under the assumption inf fu > -λ1, where λ1 is the smallest eigenvalue of u = -(pu′)′ with the boundary conditions, unique existence theorems of solution for the continuous problem and a discretized system with not necessarily uniform nodes are given as well as error estimates. The results generalize three theorems of Lees for u″ = f(x, u), 0 ≤ x ≤ 1, u(0) = α, u(1) = β.

    Original languageEnglish
    Pages (from-to)293-313
    Number of pages21
    JournalJapan Journal of Industrial and Applied Mathematics
    Volume23
    Issue number3
    Publication statusPublished - 2006 Oct

    Fingerprint

    Smallest Eigenvalue
    Two-point Boundary Value Problem
    Semilinear
    Existence Theorem
    Boundary value problems
    Error Estimates
    Boundary Value Problem
    Boundary conditions
    Generalise
    Vertex of a graph
    Theorem
    Form

    Keywords

    • Discretization
    • Error estimates
    • Existence of solution
    • Theorems of Lees
    • Tow-point boundary value problems

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

    Cite this

    On three theorems of lees for numerical treatment of semilinear two-point boundary value problems. / Yamamoto, Tetsuro; Oishi, Shinichi.

    In: Japan Journal of Industrial and Applied Mathematics, Vol. 23, No. 3, 10.2006, p. 293-313.

    Research output: Contribution to journalArticle

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