APPLICATION OF THE KANTOROVICH VARIATION METHOD ON THE EXAMPLE OF SOLUTION OF THE TWO-DIMENSIONAL NON-STATIONARY WAVE EQUATION
In this paper, using the example of solving a two-dimensional nonstationary wave equation, a description of the application of the procedure for direct minimization of a functional by reduction to a system of ordinary differential equations is given. This procedure is called the Kantorovich method. The considered wave equation is used in various subject areas, for example, in the theory of elasticity. Therefore, finding its solution is of practical interest. The paper analyzes the dynamics of an elastic membrane with an external harmonic concentrated load. Accurate determination of the deflection value of a rectangular membrane-element at the site of the action of a harmonic concentrated load during non-stationary vibrations is an extremely important task in the design of elastic sensitive elements of modern micromechanical transducers. The proposed source code in the Maple language contains many comments to help you understand how a given mathematical model of an object can be modified. In addition, the solution can be displayed graphically, which makes it easy to analyze for its dependence on coordinate functions and their number.