Geodesic
A numerical solution of an inverse boundary value problem of heat conduction using the Volterra equations of the first kind
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 3, pp. 327-335

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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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     author = {S. V. Solodusha and N. M. Yaparova},
     title = {A numerical solution of an inverse boundary value problem of heat conduction using the {Volterra} equations of the first kind},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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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. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 3, pp. 327-335. http://geodesic.mathdoc.fr/item/SJVM_2015_18_3_a6/