Accurate Difference Methods for Linear Ordinary Differential Systems Subject to Linear Constraints

Abstract

We consider the general system of n first order linear ordinary differential equations y'(t)=A(t)y(t)+g(t), a<t< b, subject to "boundary" conditions, or rather linear constraints, of the form Σ^(N)_(ν=1) B_(ν)y(τ_ν)=β 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 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).)