Finite Section Method for Linear Ordinary Differential Equations

Sufficient conditions are given for the solution of a linear ordinary differential equation on the half line to be obtained as the limit of solutions of corresponding equations on finite intervals. Both the time-variant and the time-invariant case are considered, and in the latter case the sufficient conditions referred to above are also shown to be necessary. Included are applications to a differential equation that appears in linear transport theory, and to integral equations with semi-separable kernels