NUMERICAL SOLUTION OF THE BOUNDARY PROBLEM FOR A MODEL PSEUDO-PARABOLIC-HYPERBOLIC FOURTH ORDER PARTIAL DERIVATIVE EQUATION

Abstract

  This article studies the numerical solution of boundary value problems for a model fourth-order pseudoparabolic-hyperbolic equation with individual derivatives. The subject of the study is to obtain a numerical solution of exact boundary value problems for higher order differential equations. The goal of this work is to learn how to obtain numerical solutions to boundary value problems for model pseudo-parabolic-hyperbolic fourth-order partial differential equations. The study used the finite difference method or mesh method to solve the differential equations numerically. The existence and uniqueness of a solution to the boundary value problem for a model fourth-order pseudo-parabolic-hyperbolic equation is proven. Scientific and practical significance: мodel pseudo-parabolic-hyperbolic equation of the fourth order in partial derivatives, the initial and boundary conditions imposed on it were approximated, the problem was reduced to a system of linear algebraic equations, the solution to the problem was obtained in tabular and graphical form using the grid method. The results obtained can be used in teaching undergraduates and students studying applied mathematics.