**Abstract**

The chapter contains information about new approaches to solving boundary value problems for differential equations. It introduces a new method of moving nodes. Based on the approximation of differential equations (by the finite difference method or the control volume method), introducing the concept of a moving node, approximately analytical solutions are obtained. To increase the accuracy of the obtained analytical solutions, multipoint moving nodes are used. The moving node method is used to construct compact circuits. The moving node method allows you to investigate the diskette equation for monotonicity, as well as the approximation error of the differential equation. Various test problems are considered.

**Keywords:** finite difference, boundary value problem, moving node, approximation, differential equations, difference equation, approximation error, several moving nodes, compact schemes, convective-diffusion, finite volume
