ACCURATE DIFFERENCE METHODS FOR LINEAR ORDINARY DIFFERENTIAL SYSTEMS SUBJECT TO LINEAR CONSTRAINTS

It is shown that unique continuous solution, with piecewise smooth derivatives exists if and only if specific matrix is nonsingular; some sufficient conditions, which may be of practical utility, to insure nonsingularity of this matrix are presented; simple difference scheme approximating general system of equations on nonuniform net is shown to have solution, given explicitly, whenever boundary value problem has unique solution and mesh is sufficiently fine; it is concluded that all results apply to more general (integral) boundary conditions or constraints.