文献类型：期刊文献

英文题名：A stable minimum residual method with fractional cubic splines for space fractional advection-dispersion equations

作者：Zhang, Jian[1];Du, Hong[1];Guan, Chaoyue[2]

机构：[1]Guangdong Ocean Univ, Coll Math & Comp Sci, Zhanjiang 524000, Guangdong, Peoples R China;[2]Harbin Normal Univ, Sch Math Sci, Harbin 150025, Heilongjiang, Peoples R China

年份：2026

卷号：72

期号：2

外文期刊名：JOURNAL OF APPLIED MATHEMATICS AND COMPUTING

收录：SCI-EXPANDED(收录号：WOS:001653303300003)、、EI(收录号：20260119858658)、Scopus(收录号：2-s2.0-105026337619)、WOS

语种：英文

外文关键词：Fractional cubic spline; Space fractional advection-dispersion equation; Minimum residual method; Reproducing kernel functions; Second-order stable scheme

外文摘要：This study focuses on the space fractional advection-dispersion equation. We develop a stable second-order fractional cubic spline minimum residual method (FCS-MRM) based on second-generation reproducing kernel functions. To the best of our knowledge, this is the first attempt to construct fractional cubic spline functions using reproducing kernel theory. This approach significantly simplifies the function construction process and enhances flexibility. By reformulating the equation under homogeneous boundary conditions, a unified theoretical framework is established. Time discretization is achieved via a second-order finite difference scheme, while the spatial solution is represented using fractional cubic spline basis functions. A residual functional is minimized to obtain the approximate solution. Convergence, error behavior, and stability are rigorously analyzed and proven. Numerical experiments confirm the accuracy and robustness of the proposed method. In a series of benchmark problems, the proposed method demonstrates superior performance compared to classical approaches. These include integer-order cubic splines, finite difference schemes, alternating direction implicit methods based on Crank-Nicolson, and reproducing kernel particle methods. The method consistently yields significantly lower errors.