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]; Yang, Xinyue[2]; Chen, Zhong[3]

机构：[1] College of Mathematics and Computer Science, GuangDong Ocean University, Guangdong, Zhanjiang, 524000, China; [2] College of earth and environmental sciences, Lanzhou University, Gansu, Lanzhou, 730000, China; [3] Department of Mathematics, Harbin Institute of Technology at Weihai, Shandong, 264209, China

年份：2023

外文期刊名：SSRN

收录：EI(收录号：20230136057)

语种：英文

外文关键词：Diffusion - Interpolation - Nonlinear equations - Wave equations

外文摘要：It's well known that the meshless method is an effective method for solving fractional differential equations on different types of regular or irregular domains. However, some common functions are often defined on rectangular domains, such as Legendre wavelets bases functions, B-spline functions, etc. It caused that these functions cannot be applied to some meshless methods. In the paper, we are motivated to develop a new meshless method of solving the time-fractional mixed nonlinear diffusion and diffusion-wave equation on arbitrary domains by a skillful extension technology. The meshless method could use the well-known Legendre mulitiwavelets bases toobtain the best approximate solution by searching the minimum of Ε-approximate solutions in the reproducing kernel space. It doesn’t have to calculate complicated shape functions or other local bases functions. Construction of the reproducing kernel Legendre mulitiwavelets bases in the paper are also easy. Numerical examples reported on rectangular domains and domains with a curved boundary further verified that the method is efficient and attains the better accuracy. ? 2023, The Authors. All rights reserved.