Contribution à la méthode des équations aux différences

SummaryLet a linear boundary value problem or an eigenvalue problem be given, in one or more dimensions. I look for such a construction of a corresponding difference equation that, in the case of ordinary differential equations with constant coefficients, its solutions beexactly those of the continuous problem.—This ‘trivial’ case is first investigated and several methods are pointed out; these are then applied to: (a) ordinary differential equations with variable coefficients (‘method of local perturbations’); (b) vibration problems for membranes and clamped plates.