文献类型：期刊文献

英文题名：Adaptive spectral solver for Riesz fractional reaction-diffusion equations via penalized minimum residual iteration

作者：Guan, Chaoyue[1,2];Zhang, Jian[1]

机构：[1]Guangdong Ocean Univ, Coll Math & Comp Sci, Zhanjiang 524088, Guangdong, Peoples R China;[2]Harbin Normal Univ, Sch Math Sci, Harbin 150025, Heilongjiang, Peoples R China

年份：2026

卷号：241

起止页码：431

外文期刊名：MATHEMATICS AND COMPUTERS IN SIMULATION

收录：SCI-EXPANDED(收录号：WOS:001605957300001)、、WOS

基金：This work was supported by the Zhanjiang Science and Technology Program (Grant No. 2025B01056) .

语种：英文

外文关键词：Fractional reaction-diffusion equation; Weighted Jacobi spectral method; Adaptive Levenberg-Marquardt iteration; Boundary penalty enforcement

外文摘要：A high-order solver is presented for two-dimensional Riesz fractional nonlinear reaction-diffusion equations. It employs a midpoint starter and a three-point backward differentiation formula (BDF2) to achieve second-order temporal accuracy, together with a weighted Jacobi spectral approximation that delivers nearly exponential spatial convergence for analytic solutions. After Newton linearization, each correction is obtained via a penalized Levenberg-Marquardt minimum residual method (PLM-MRM). This iteration adaptively enforces boundary conditions without requiring boundary-fitted basis functions. We establish stability and rigorous a priori error bounds. Numerical experiments over a wide range of fractional orders confirm these rates and drive the residual to machine precision within a few PLM-MRM sweeps. Compared with a conventional LM update, global errors are reduced by up to 35%, and by one to two orders of magnitude relative to Galerkin-BDF or Crank-Nicolson (CN) baselines. For a given accuracy, the scheme allows time steps up to about four times larger than a recent fourth-order CN method.