Numerical research of the Barenblatt – Zheltov – Kochina model on the interval with Wentzell boundary conditions

In terms of numerical research, we study the Barenblatt – Zheltov – Kochina model, which describes dynamics of pressure of a filtered fluid in a fractured-porous medium with the general Wentzell boundary conditions. Based on the theoretical results associated with Galerkin method, we develop an algorithm and implement the numerical solution of the Cauchy-Wentzell problem on the interval $[0, 1]$. In particular, we examine the asymptotic approximation of the spectrum of the one-dimensional Laplace operator and present result of a computational experiment. In the paper, these problems are solved under the assumption that the initial space is a contraction of the space $L^2(0, 1)$.