Geodesic
Parallel sweep algorithm for solving direct and inverse problems for time-fractional diffusion equation
Numerical methods and programming, Tome 23 (2022) no. 4, pp. 275-287

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The work is devoted to construction of parallel algorithm for solving the direct initial boundary and inverse right-hand part identification problems for the time-fractional diffusion equation. Application of a priori information on the solution at the some inner point allows one to reduce the inverse problem to an initial boundary problem for the auxiliary equation. After applying the finite-difference scheme the problems are reduced to solving systems of linear algebraic equations. The developed algorithms are based on the parallel sweep method and implemented for the multicore processor using the OpenMP technology. Numerical experiments were performed to study the performance of the developed algorithms.
Mots-clés : fractional diffusion equation
Keywords: Caputo derivative, initial boundary problem, inverse problem, time-dependent right-hand part, parallel sweep method, multicore processors, OpenMP. 
@article{VMP_2022_23_4_a4,
     author = {E. N. Akimova and M. A. Sultanov and V. E. Misilov and Y. Nurlanuly},
     title = {Parallel sweep algorithm for solving direct and inverse problems for time-fractional diffusion equation},
     journal = {Numerical methods and programming},
     pages = {275--287},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2022_23_4_a4/}
}
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E. N. Akimova; M. A. Sultanov; V. E. Misilov; Y. Nurlanuly. Parallel sweep algorithm for solving direct and inverse problems for time-fractional diffusion equation. Numerical methods and programming, Tome 23 (2022) no. 4, pp. 275-287. http://geodesic.mathdoc.fr/item/VMP_2022_23_4_a4/