Summary approximation method for a third order multidimensional pseudoparabolic equation

In this paper we study the first initial-boundary value problem for a multidimensional pseudoparabolic equation of the third order. Assuming the existence of a regular solution to the problem posed, an a priori estimate is obtained in differential form, which implies the uniqueness and stability of the solution with respect to the right-hand side and initial data. A locally one-dimensional difference scheme is constructed and an a priori estimate in the difference form is obtained for its solution. The stability and convergence of the locally one-dimensional difference scheme are proved. Numerical calculations are performed using test examples to illustrate the theoretical calculations obtained in this work.