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Accurate difference methods for linear ordinary differential systems subject to linear constraints

By Herbert B. Keller

Abstract

We consider the general system of n first order linear\ud ordinary differential equations y'(t)=A(t)y(t)+g(t), a<t< b,\ud subject to "boundary" conditions, or rather linear constraints, of the form Σ^(N)_(ν=1) B_(ν)y(τ_ν)=β\ud Here y(t), g(t) and II are n-vectors and A(t), Bx,..., BN are n × n matrices. The N distinct points {τ_ν} lie in [a,b] and we only require N ≧ 1. Thus as special cases\ud initial value problems, N=1, are included as well as the general 2-point boundary value problem, N=2, with τ_1=a, τ_2=b. (More general linear constraints are also studied, see (5.1) and (5.17).

Publisher: Society for Industrial and Applied Mathematics
Year: 1969
OAI identifier: oai:authors.library.caltech.edu:34280
Provided by: Caltech Authors

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