Geodesic
The Newton--Kantorovich method in inverse source problems for production-destruction models with time series-type measurement data
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 1, pp. 57-79

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The algorithms for solving the inverse source problem for the production–destruction type systems of nonlinear ordinary differential equations with measurement data in the form of time series are presented. The sensitivity operator and its discrete analogue on the basis of adjoint equations are constructed. This operator binds the perturbations in the unknown parameters of the model to those of the measured values. The operator allows one to construct a family of quasi-linear operator equations linking the required unknown parameters and the data of the inverse problem. The Newton–Kantorovich type method with right-hand side $r$-pseudoinverse matrices is used to solve the equations. The algorithm is applied to solving the inverse source problem for the atmospheric impurities transformation model. 
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     author = {A. V. Penenko},
     title = {The {Newton--Kantorovich} method in inverse source problems for production-destruction models with time series-type measurement data},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {57--79},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2019_22_1_a4/}
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A. V. Penenko. The Newton--Kantorovich method in inverse source problems for production-destruction models with time series-type measurement data. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 1, pp. 57-79. http://geodesic.mathdoc.fr/item/SJVM_2019_22_1_a4/