Geodesic
Numerical solution to parametric identification problems for partial differential equations
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 2 (2018), pp. 33-44

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The paper proposes a numerical method for solving the problem, based on the use of the method of lines to reduce the problem to a system of ordinary differential equations with unknown parameters. Next, we use a special representation of the solution of the obtained boundary value problem for a linear system of differential equations with nonlocal conditions, by means of which the problem of parametric identification reduces to solving auxiliary boundary value problems and a system of algebraic equations. It is important to note that, unlike optimization approaches, The construction of any iterative procedures or minimizing sequences is used.
Keywords: inverse problem, method of lines, parametric identification.
Mots-clés : parabolic type equation 
@article{VKAM_2018_2_a3,
     author = {V. M. Abdullayev},
     title = {Numerical solution to parametric identification problems for partial differential equations},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {33--44},
     publisher = {mathdoc},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2018_2_a3/}
}
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V. M. Abdullayev. Numerical solution to parametric identification problems for partial differential equations. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 2 (2018), pp. 33-44. http://geodesic.mathdoc.fr/item/VKAM_2018_2_a3/