Regarding the solution of the plate theory boundary problem for domains of complex shape

Abstract

Mathematical model construction of complicate physical phenomenon often leads to the setting and solving problems of parameters optimal control in differential equations in partial derivatives. Chosen equation with boundary and initial conditions is usually mathematical model basis of the object, which is under analysis. Optimal control of right-hand side function in non-linear problem for inhomogeneous biharmonic has been investigated. With the help of various gradient methods the problems of parameters control in such equations are solved successfully. Herewith linear problem is solved with the potential method on every step. The boundary value problem of plate theory, which is reduced to a system of Fredholm integral equations of the first kind and an algorithm of self-regularization of this system, is considered. The potential method is used to solve the linear problem for the harmonic equation. Examples of numerical implementation are shown that demonstrate high computational efficiency in the case of complex form regions. Algorithm for linear boundary value problem solution with boundary integral equations overcomes this problem successfully. Physical examples of numerical implementation have been presented, analysis of obtained solutions have been conducted. Their accuracy, algorithm simplicity and time spent evidence about this approach promising for practical results obtaining in plate theory and mathematical physics problems successful numerical solving.