A numerical solution of an inverse boundary value problem of heat conduction using the Volterra equations of the first kind
Svetlana V. Solodusha1, Natalia M. Yaparova2
1Melentiev Energy Systems Institute SB RAS, Russia Department of Applied Mathematics, Irkutsk, Russia
2South Ural State University, Chelyabinsk, Russia
Keywords: Volterra integral equations, numerical solution, product integration method
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.
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