NUMERICAL SOLUTION OF BOUNDARY VALUE PROBLEMS FOR A HYPERBOLIC EQUATION OF FOURTH ORDER

Abstract

The article considers the solution of the Gursa problem by the grid method for a fourth-order hyperbolic equation with three-fold characteristics. From the beginning, with the help of approximation, finite differences of derivatives and a grid equation are obtained. Using a grid equation and imposed conditions, a linear system of algebraic equations is obtained with respect to unknown values of the function in the grid. The finite difference method is used. The essence of this most universal numerical method is that the desired set of numbers is taken as a table of solution values at the points of a certain set, usually called a grid. To calculate the required table, algebraic equations are used, which approximately replace the differential equation. The main purpose of the article is to demonstrate, by approximating and using the grid method, the reduction to difference schemes, i.e., a system of algebraic equations, the Goursat problem. The existence and uniqueness of solutions to the tasks are proved.