Differentical equations, dynamical systems and optimal control

Approximate solution of the smooth transition equation

V. A. Lukianenko

V.I. Vernadsky Crimean Federal University, Prospekt Vernadskogo ave., Simferopol, Republic of Crimea, 295007, Russia

Abstract: The problems of stability and the approximate solution of the integral smooth transition equation first introduced and studied by Yu.I. Chersky are considered. Using the solution of the smooth transition equation under classical assumptions, it is possible to construct the solution of the equation under weaker constraints on the kernels. For the approximate solution, an error estimation and a theorem on the uniqueness and sustainability are provided.

Keywords: smooth transition integral equation, approximate solution, iterative algorithms, stability.

UDC: 517.44

MSC: 45E10, 30E25, 92K05

Received February 3, 2020, published November 13, 2020

Language: English

DOI: 10.33048/semi.2020.17.125

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