«Automation and Informatization of the fuel and energy complex»

The possibility of supplementing the variational methods of differential equations solution, by applying the function inverse to the solution

UDC: 519.223.5:519.246.85
DOI: 10.33285/2782-604X-2022-7(588)-45-52

Authors:

¹ Samara State Technical University, Samara, Russia

Keywords: data processing, variational methods, differential equations, method of additional boundary conditions, collocation method, least squares method, inverse functions

Annotation:

The article proposes the simultaneous use of both an approximate solution and a function inverse to it, when solving differential equations by the variational methods application. Based on the type of the equation to be solved and the known relation between the derivatives of mutually inverse functions, a differential equation is obtained, which should be satisfied by the function inverse to the approximate solution. This equation can be solved by applying the variational method together with the original one. Since the approximate solution and the function inverse to it (as well as their derivatives) are interrelated and depend on one and the same parameters, it allows noticeable (approximately twice) increase of the number of conditions that the selected parameters should satisfy. The redundancy of such conditions system can be used not only to increase the reliability of the approximate solution’s parameters selection, but also to obtain additional, more detailed information about the properties of the applied mathematical model.

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