TY - GEN
T1 - Time Stepping Adaptation for Subdiffusion Problems with Non-smooth Right-Hand Sides
AU - Franz, Sebastian
AU - Kopteva, Natalia
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
PY - 2025
Y1 - 2025
N2 - We consider a time-fractional subdiffusion equation with a Caputo derivative in time, a general second-order elliptic spatial operator, and a right-hand side that is non-smooth in time. The presence of the latter may lead to locking problems in our time stepping procedure recently introduced in [J. Comp. Appl. Math., 427(115122), 2023] and [Appl. Math. Lett., 123: Paper No. 107515, 8, 2022]. Hence, a generalized version of the residual barrier is proposed here to rectify the issue. We also consider related alternatives to this generalized algorithm, and, furthermore, show that this new residual barrier may be useful in the case of a negative reaction coefficient.
AB - We consider a time-fractional subdiffusion equation with a Caputo derivative in time, a general second-order elliptic spatial operator, and a right-hand side that is non-smooth in time. The presence of the latter may lead to locking problems in our time stepping procedure recently introduced in [J. Comp. Appl. Math., 427(115122), 2023] and [Appl. Math. Lett., 123: Paper No. 107515, 8, 2022]. Hence, a generalized version of the residual barrier is proposed here to rectify the issue. We also consider related alternatives to this generalized algorithm, and, furthermore, show that this new residual barrier may be useful in the case of a negative reaction coefficient.
UR - https://www.scopus.com/pages/publications/105004254818
U2 - 10.1007/978-3-031-86173-4_31
DO - 10.1007/978-3-031-86173-4_31
M3 - Conference contribution
AN - SCOPUS:105004254818
SN - 9783031861727
T3 - Lecture Notes in Computational Science and Engineering
SP - 305
EP - 312
BT - Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 1 - European Conference
A2 - Sequeira, Adélia
A2 - Silvestre, Ana
A2 - Valtchev, Svilen S.
A2 - Janela, João
PB - Springer Science and Business Media Deutschland GmbH
T2 - European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2023
Y2 - 4 September 2023 through 8 September 2023
ER -