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This article is cited in 14 scientific papers (total in 14 papers)
A numerical solution of an inverse boundary value problem of heat conduction using the Volterra equations of the first kind
S. V. Solodushaa, N. M. Yaparovab a Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences, 130 Lermontov str., Irkutsk, 664033, Russia
b South Ural State University, 76 Lenin pr., Chelyabinsk, 454080, Russia
Abstract:
We consider an inverse boundary value problem of heat conduction. To solve it, we propose a new approach based on the Laplace transform. This approach allows us to confine the original problem to solving the Volterra equations of the first kind. We have developed algorithms of the numerical solution to the resulting integral equations. The algorithms developed are based on the application of the product integration method and the quadrature of middle rectangles. A series of test calculations were performed to test the efficiency of the numerical methods.
Key words:
Volterra integral equations, numerical solution, product integration method.
Received: 07.07.2014 Revised: 17.10.2014
Citation:
S. V. Solodusha, N. M. Yaparova, “A numerical solution of an inverse boundary value problem of heat conduction using the Volterra equations of the first kind”, Sib. Zh. Vychisl. Mat., 18:3 (2015), 327–335; Num. Anal. Appl., 8:3 (2015), 267–274
Linking options:
https://www.mathnet.ru/eng/sjvm585 https://www.mathnet.ru/eng/sjvm/v18/i3/p327
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