Parallel Direct and Iterative Methods for Solving the Time-Fractional Diffusion Equation on Multicore Processors
Sultanov M.A. Akimova E.N. Misilov V.E. Nurlanuly E.
February-1 2022MDPI
Mathematics
2022#10Issue 3
The work is devoted to developing the parallel algorithms for solving the initial boundary problem for the time-fractional diffusion equation. After applying the finite-difference scheme to approximate the basis equation, the problem is reduced to solving a system of linear algebraic equations for each subsequent time level. The developed parallel algorithms are based on the Thomas algorithm, parallel sweep algorithm, and accelerated over-relaxation method for solving this system. Stability of the approximation scheme is established. The parallel implementations are developed for the multicore CPU using the OpenMP technology. The numerical experiments are performed to compare these methods and to study the performance of parallel implementations. The parallel sweep method shows the lowest computing time.
Accelerated over-relaxation method , Caputo fractional derivative , Finite-difference scheme , Parallel computing , Parallel sweep method , Thomas algorithm , Time-fractional diffusion equation
Text of the article Перейти на текст статьи
Department of Mathematics, Faculty of Natural Science, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan, 160200, Kazakhstan
Krasovskii Institute of Mathematics and Mechanics, Ural Branch of RAS, S. Kovalevskaya Street 16, Ekaterinburg, 620108, Russian Federation
Department of Information Technologies and Control Systems, Institute of Radioelectronics and Information Technology, Ural Federal University, Mira Street 19, Ekaterinburg, 620002, Russian Federation
Department of Mathematics
Krasovskii Institute of Mathematics and Mechanics
Department of Information Technologies and Control Systems
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026