On finite-difference methods for the numerical solution of boundary-value problems

We consider the application of finite-difference methods to the numerical solution of boundary-value problems. In particular we are concerned to study the feasibility and con­vergence of the difference-correction method for the solution of partial differential equations of elliptic type. These topics form the subject matter for §§ 3 to 6. The material of the first two sections is intended to serve as a preliminary for the main discussion. The topics considered here are finite difference formulae for numerical differentiation, and finite difference methods for the solution of partial differential equations.