Identification Method of Operational Control the Process a Numerical Solution of Differential Equation

• Дата: 2018
• Автори: Верлань, Анатолий Федорович, Положаенко, Сергей Анатолиевич, Протасов, Сергей Юриевич
• Формат: Стаття
• Мова: rus
• Опубліковано: Кам'янець-Подільський національний університет імені Івана Огієнка 2018
• Онлайн доступ: http://mcm-math.kpnu.edu.ua/article/view/159251
• Назва журналу: Mathematical and computer modelling. Series: Physical and mathematical sciences

In computer studies of dynamic problems, numerical methods for solving differential equations are usually used. Essential importance in numerical calculations is guaranteed accuracy of the calculated solution, which depends on the accuracy of the computer used and the influence on the decision of inevitable errors of input data and rounding errors. Although the computational rules are built on the basis of the conditions for ensuring their possible growth with respect to the error, however, with a large number of steps, the deviation of the solution obtained by a numerical method from the exact one can be quite significant.Obtaining satisfactory estimates of the operational numerical solution of differential equations is a rather complicated task, which in many practical cases cannot be solved. Thus, an urgent task from a computational point of view is the development of approaches and methods that allow control of the computational process.In this paper, we consider the possibility of controlling the error of numerical solution by using the methods of parametric identification, which are widely used in solving practical problems of identifying linear and nonlinear systems. At the same time, the accuracy of the control should not depend on the reasons causing the error of the decision. The control process itself consists of the following steps: the parameters of the equations for which the resulting numerical solution is accurate are restored with some accuracy. The estimated parameters (the coefficients are compared with the coefficients of the original equations; the difference of the coefficients is the information that is used to evaluate the behavior of the solution on the restoration site (the recovery section is the segment of the numerical solution that is used for parametric identification).