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

Tetsuro Yamamoto, Shinichi Oishi

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    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

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    Keywords

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

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

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