The solution of problem convection-diffusion equation by way of control volume method is considered. Approximate solution of problem is received. Three point scheme of high resolution is constructed.

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.

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In our papers by us [11],[12] a new method of moving nodes (MMN) was introduced to obtain an approximate analytical solution and construct compact schemes for a one-dimensional convective-diffusion problem. It is proposed to improve the scheme in a three-point pattern. As an initial scheme, a counter flow with one-sided differences is taken. In the QUICK scheme [5], quadratic up flow interpolation is used to determine convective flow. Here we use the solution obtained by the upwind scheme based on MMN. In our above works, the improvement in the accuracy of difference schemes was obtained on the basis of using the method of multi point MMN. In this work, it is proposed to improve the accuracy of the constructed difference schemes using the three point MMN. This is achieved using a more accurate solution to the unknown function on the edge of the considered control volume, the algorithm of which is described in detail in this work.

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