Geodesic
Method for solving an inverse term source problem based on the Laplace transform
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 5 (2016) no. 3, pp. 20-35

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In this contribution, the method for solving the inverse source problem for parabolic partial differential equations with Dirichlet and Neumann boundary conditions is proposed. We reduce this problem to solving Volterra integral equation of the first kind via applications of the Laplace transforms. Then we use the regularization technique for numerical solving for the obtained equation. The integral equation describe the explicit dependence of the unknown source term on the Neumann boundary condition. The proposed approach allows to eliminate the unstable inverse Laplace transform from numerical scheme and simplify the computational procedure provided the basis to develop method for solving an inverse source problem. This approach to solving the inverse source problem is used for the first time. The efficiency of method and accuracy of the numerical solutions were evaluated by means of computational experiment.
Keywords: inverse source problem, Volterra integral equation, numerical method.
Mots-clés : Laplace transform 
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     author = {N. M. Yaparova},
     title = {Method for solving an inverse term source problem based on the {Laplace} transform},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a Vy\v{c}islitelʹna\^a matematika i informatika},
     pages = {20--35},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURV_2016_5_3_a1/}
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N. M. Yaparova. Method for solving an inverse term source problem based on the Laplace transform. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 5 (2016) no. 3, pp. 20-35. http://geodesic.mathdoc.fr/item/VYURV_2016_5_3_a1/