Approximate-analytical Control Volume Method for Solving Boundary Value Problems

Abstract

It is known that the control volume method is widely used in numerical analysis for solving boundary value problems. Using this approach allows obtaining an approximate-analytical method for obtaining a solution to boundary value problems. A method for averaging boundary value problems over the volume being moved is proposed. The control volume is unique and movable in the area under consideration. The solution of the problem is obtained by averaging the differential equation over the volume being moved. For two-dimensional boundary value problems, it is also recommended to average over one variable. On the basis of which an ordinary differential is obtained and the solution of which gives a better solution to the problem. Examples are given.