Numerical solution of blow-up behavior for time-fractional diffusion-wave equations
发布时间：2026-10-02
点击次数：
DOI码：10.1016/j.physd.2026.135434
发表刊物：Physica D: Nonlinear Phenomena
摘要：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.
第一作者：Shreya Singh, Rajesh K. Pandey
论文类型：期刊论文
通讯作者：Yufeng Xu
学科门类：理学
一级学科：数学
文献类型：J
卷号：498
页面范围：1--17
是否译文：否
发表时间：2026-09-22
收录刊物：SCI
发布期刊链接：https://www.sciencedirect.com/science/article/pii/S0167278926003301