TY - JOUR
T1 - On three theorems of lees for numerical treatment of semilinear two-point boundary value problems
AU - Yamamoto, Tetsuro
AU - Oishi, Shin'ichi
PY - 2006/10
Y1 - 2006/10
N2 - 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, α0+α1 > 0, β0+β 1 > 0, α0+β0 > 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.
AB - 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, α0+α1 > 0, β0+β 1 > 0, α0+β0 > 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.
KW - Discretization
KW - Error estimates
KW - Existence of solution
KW - Theorems of Lees
KW - Tow-point boundary value problems
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U2 - 10.1007/BF03167596
DO - 10.1007/BF03167596
M3 - Article
AN - SCOPUS:33845987554
VL - 23
SP - 293
EP - 313
JO - Japan Journal of Industrial and Applied Mathematics
JF - Japan Journal of Industrial and Applied Mathematics
SN - 0916-7005
IS - 3
ER -