Тип публикации: доклад, тезисы доклада, статья из сборника материалов конференций
Конференция: International Conference on Marchuk Scientific Readings 2020, MSR 2020
Год издания: 2021
Идентификатор DOI: 10.1088/1742-6596/1715/1/012044
Аннотация: When estimating the error of numerical solutions of ordinary differential equations, it is proposed to use the regularization of error estimation algorithms for approximate solutions. Regularization is considered as the use of additional a priori information about the numerical solution. A priori information is estimated by the metПоказать полностьюhod of the inverse error analysis, which implements the transformation of the statement of the problem of evaluating the accuracy of the numerical solution. In this case, the problem is selected so that the approximate solution is the exact solution of the transformed problem, close to the original problem. It is also possible to add some additional restrictions to the conditions of the problem. This allows us to solve the incorrectly posed problems of estimating errors in numerical solutions, which in most cases are unstable. It is known that earlier in the numerical solution of linear algebra problems the inverse error analysis was used by Wilkinson J. and also Voevodin V.V., application of the inverse error analysis in other areas of numerical analysis can be noted. Using direct and inverse error analysis Voevodin V.V. effectively calculated majorants of rounding errors in the most important methods of linear algebra and significantly developed the method of inverse error analysis.. However, the regularization process associated with the reverse analysis of errors has not been previously studied. The article discusses the characteristics of regularization in the inverse analysis of errors in the numerical solution of ordinary differential equations with initial data. The regularization of error estimation algorithms has advantages in the numerical solution of ordinary differential equations of real models of physics and technology. © 2021 Institute of Physics Publishing. All rights reserved.
Журнал: Journal of Physics: Conference Series
Выпуск журнала: Vol. 1715, Is. 1
Номера страниц: 12044
ISSN журнала: 17426588
Издатель: IOP Publishing Ltd