Geodesic
Numerical method for solving an inverse problem for nonlinear parabolic equation with unknown initial conditions
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 5 (2016) no. 2, pp. 43-58

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The paper is devoted to the inverse problem for a nonlinear parabolic equation with unknown initial conditions. A computational scheme for solving this problem is proposed. This approach allows obtain the numerical solution in internal points of domain and the unknown boundary function. The proposed scheme is based on the using of finite-difference equations and regularization technique. We investigate the stability of computational method. We obtained the dependence of stability on the discretization steps and level error of the initial data The proposed scheme proved the basis for development of numerical method and for the computational experiment. The experimental results are also presented in this paper, and confirm the effectiveness of the method.
Keywords: inverse problem, numerical method, regularization method, error estimate, computational scheme. 
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     author = {N. M. Yaparova},
     title = {Numerical method for solving an inverse problem for nonlinear parabolic equation with unknown initial conditions},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a Vy\v{c}islitelʹna\^a matematika i informatika},
     pages = {43--58},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURV_2016_5_2_a3/}
}
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N. M. Yaparova. Numerical method for solving an inverse problem for nonlinear parabolic equation with unknown initial conditions. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 5 (2016) no. 2, pp. 43-58. http://geodesic.mathdoc.fr/item/VYURV_2016_5_2_a3/