 Fast linearized compact difference scheme for a two-dimensional nonlinear time-fractional diffusion-wave equationMeng Wang, Lijuan Nong and An Chen Mathematics and Computers in Simulation (MATCOM), 2026, vol. 240, issue C, 889-903 Abstract: In this paper, we propose an efficient compact difference scheme for solving a two-dimensional nonlinear time-fractional diffusion-wave equation where the fractional derivative is in the Caputo sense and the nonlinear term is given by the sine function. We first transform the original problem into a low-order system by applying a symmetric fractional-order reduction method. To address the initially weak singularity of the problem solution and improve computational efficiency, we discrete the resulted system with a fast nonuniform meshes-based L2-1σ formula in time and the compact difference method in space to obtain the fully finite difference scheme. The corresponding stability and error estimate are provided rigorously. Finally, extensive numerical examples are demonstrated, including numerical simulations for the collisions of four circular solitons to verify the accuracy and effectiveness of our scheme. Keywords: Time-fractional diffusion-wave equation; Fast nonuniform L2-1σ formula; Compact difference method; Stability; Error estimate (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:240:y:2026:i:c:p:889-903 DOI: 10.1016/j.matcom.2025.08.015 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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