Mathematical analysis and symmetric fractional-order reduction method for diffusion-wave equations

Abstract

In this work, our aim is to introduce a symmetric fractional-order reduction (SFOR) method to develop numerical algorithms on nonuniform temporal meshes for fractional wave equations under lower regularity assumptions. The $L$-type methods--including $L1$ and $L2$-$1_{\sigma }$ schemes--are specifically designed for diffusion-wave equations, and we propose novel optimal parameter selections tailored to nonuniform meshes. Finally, several numerical experiments are conducted to validate the efficiency and accuracy of the algorithms.

arXiv comment25 pages