文献类型：期刊文献

英文题名：A New Method of Solving the Time-Fractional Mixed Nonlinear Diffusion and Diffusion-Wave Equation

作者：Du, Hong[1];Chen, Zhong[2];Yang, Tiejun[3]

机构：[1]Guangdong Ocean Univ, Coll Math & Comp Sci, Zhanjiang 524000, Peoples R China;[2]Harbin Inst Technol, Dept Math, Weihai 264209, Peoples R China;[3]Guangdong Ocean Univ, Coll Coastal Argricultural Sci, Zhanjiang 524000, Peoples R China

年份：2026

卷号：10

期号：9

外文期刊名：FRACTAL AND FRACTIONAL

收录：SCI-EXPANDED(收录号：WOS:001890395800001)、、Scopus(收录号：2-s2.0-105051581836)、WOS

基金：GuangDong Ocean University (Grant No. R20050).

语种：英文

外文关键词：fractional equations; reproducing kernel mulitiwavelets; arbitrary domains; nonlinear diffusion equations

外文摘要：It is well known that meshless methods are effective for solving fractional differential equations on both regular and irregular domains. However, many commonly used basis functions such as Legendre wavelets and B-splines are naturally defined on rectangular domains, which limits their applicability in certain meshless frameworks. In this paper, we are motivated to develop a new meshless method for solving the time-fractional mixed nonlinear diffusion and diffusion-wave equation on arbitrary domains, by employing a skillful extension technique. The proposed method utilizes the well-known Legendre multiwavelets to obtain the best approximate solution by seeking the minimum of approximate solutions within a reproducing kernel space. This approach avoids the need to compute complicated shape functions or other local basis functions. Moreover, the construction of the reproducing kernel Legendre multiwavelet bases presented in this paper is straightforward. Numerical examples on both rectangular domains and domains with curved boundaries confirm that the method is efficient and achieves high accuracy.