ПОСТРОЕНИЕ СОПРЯЖЕННОЙ ЗАДАЧИ В НОВОМ СМЫСЛЕ, СООТВЕТСТВУЮЩЕМ ГРАНИЧНОЙ ЗАДАЧЕ ДЛЯ ОБЫКНОВЕННОГО ЛИНЕЙНОГО ДИФФЕРЕНЦИАЛЬНОГО УРАВНЕНИЯ С ПОСТОЯННЫМИ КОЭФФИЦИЕНТАМИ ВТОРОГО ПОРЯДКА (100,00 руб.)

Этот метод основан на необходимых условиях, получаемых из формулы Лагранжа и ее аналога. <...> Ключевые слова: граничная задача, фундаментальное решение, основные соотношения, необходимые условия, сопряженная задача. <...> CONSTRUCTION OF A PROBLEM ADJIONT IN A NEW SENSE TO THE BOUNDARY VALUE PROBLEM FOR A CONSTANT COEFFICIENT SECOND ORDER ORDINARY LINEAR DIFFERENTIAL EQUATION In this paper, the boundary condition of the adjoint problem for a second order ordinary differential equation is constructed by a new method. <...> This method is based on necessary conditions given by the main relations obtained from the Lagrange method and its analogy. <...> Thus, boundary values of the desired function and its derivatives are determined from the system obtained by adjoining the necessary conditions to the given boundary conditions. <...> Key words: boundary value problem, fundamental solution, main relations, necessary conditions, adjoint problem. <...> Introduction: It is known that the construction of the adjoint problem to the boundary value problem stated for ordinary linear differential equation was obtained in [1] by using the Lagrange formula. <...> It should be noted that, the function being searched and the boundary values of its derivative are determined from the systems obtained from expressions adjoined to the given boundary conditions with arbitrary coefficients. <...> Since the arbitrary coefficients in adjoined expressions are contained in the boundary conditions of the adjoint problem, the adjoint problem is not determined uniquely. <...> Therefore, in order to determine the boundary conditions ( the domain of definition of the operator) of the adjoint problem, we use the scheme given in [2]-[3]. <...> For this purpose, the main relations are obtained using the fundamental solution. <...> The maximum number of linear independent necessary conditions equals the amount of the given boundary conditions. <...> Our goal is to construct a boundary value problem adjoint to boundary value problem (1)-(2). <...> Lagrange formula is the basic expression for this purpose, similar to [1]. <...> Let us adjoin to the given boundary conditions (with arbitrary constants) two more expressions:   4,1 (k) jk y a  jky b l y , ( ) k1 When j 1, j 2 then we get (2) boundary conditions, in case j  3, j 4 we <...>