DOI number:10.1016/j.physd.2026.135434
Journal:Physica D: Nonlinear Phenomena
Abstract:The blow-up phenomenon for fractional evolution equations poses profound analytical difficulties, making exact characterization a particularly elusive task. In this paper, we propose an algorithm to handle a class of semilinear fractional evolution equations, where the temporal derivative contains a first-order partial derivative and a Caputo fractional derivative with order between one and two, with a nonlinear source term exhibiting exponential singularity at infinity. The symmetric fractional-order reduction technique is utilized to convert the original problem into an equivalent coupled system by decomposing the Caputo fractional derivative of order $\beta$ $(1 < \beta < 2)$ into fractional derivatives of order $\beta/2$. An efficient numerical framework is then developed by integrating the fast Alikhanov $L2$-$1_{\sigma}$ scheme, which utilizes the sum-of-exponentials approximation for the Caputo derivative of order $\beta/2$, with an adaptive time-stepping approach. Spatial derivatives are discretized using the local radial basis function-generated finite difference (in short, local RBF-FD) method. The stability and convergence of the proposed scheme are proved under the frozen source term assumption. Several comprehensive numerical experiments are carried out to confirm the theoretical results, and the blow-up time, along with the impact of different model parameters on the blow-up dynamics are examined in detail.
First Author:Shreya Singh, Rajesh K. Pandey
Indexed by:Journal paper
Correspondence Author:Yufeng Xu
Discipline:Natural Science
First-Level Discipline:Mathematics
Document Type:J
Volume:498
Page Number:1--17
Translation or Not:no
Included Journals:SCI
Links to published journals:https://www.sciencedirect.com/science/article/pii/S0167278926003301