On the convergence of difference schemes for third-order pseudoparabolic equations with degeneracy

In this work, a difference scheme is constructed for a third-order pseudoparabolic equation with degeneracy. To solve the difference problem, an a priori estimate is obtained, which implies that the solution of the difference problem converges to the solution of the corresponding differential problem with a speed of $O(h^{3/2} + \tau^2)$, where $h$ and $\tau$ are the mesh parameters.