The one-dimensional problem of plane-radial filtration is under consideration. The process is described by means of the equation of continuity and Darcy's law. The problem is solved with the help of the finite difference method using both the uniform and the non-uniform types of meshes. Porosity, viscosity and the penetrability coefficients are considered constants. It is shown that for the problem analyzed the use of implicit difference scheme is more appropriate. The calculation of maximal relative error and average relative error depending on the number of knots according to time and space is made. It is shown that if the gradient of the calculating function on the uniform mesh is the monotone function according to space variable, it is possible to select the non-uniform mesh on the bases of the mesh non-uniformity criterion Θ so that to keep the exactness of calculations taking into account the possibly minimal amount of knots. The circumstance mentioned is of special importance while solving the more complicated nonlinear problems by means of the iteration method, when each iteration demands the solution of the problem of the similar kind. The estimations of errors depending on the criterion Θ are obtained. The results of the calculating experiments are given in the article.

Рассматривается одномерная задача плоскорадиальной фильтрации. Процесс описывается с помощью уравнения неразрывности и закона Дарси. Задача решается с помощью метода конечных разностей с использованием как равномерной, так и неравномерной сетки. Проведена оценка погрешности используемого алгоритма, в зависимости от числа шагов по времени и пространству. Предложен способ, позволяющий расположить узлы на неравномерной сетке на основании критерия неравномерности сетки Θ так, чтобы сохранить точность вычислений при возможно минимальном количестве узлов.