Numerical solution for a class of space-time fractional equation by the piecewise reproducing kernel method

• Published in: International journal of computer mathematics Vol. 96; no. 10; pp. 2100 - 2111
• Main Authors: Wang, Yu-Lan, Jia, Li-na, Zhang, Hao-lu
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.10.2019; Taylor & Francis Ltd
• Subjects: approximate solution; Caputo fractional derivative; Error analysis; Exact solutions; Kernels; Mathematical analysis; Partial differential equations; Piecewise technique; reproducing kernel space; space-time fractional equation; Stability
• ISSN: 0020-7160; 1029-0265
• DOI: 10.1080/00207160.2018.1544367

Due to the non-locality of fractional derivative, the analytical solution and good approximate solution of fractional partial differential equations are usually difficult to get. Reproducing kernel space is a perfect space in studying this type of equations, however the numerical results of equations by using the traditional reproducing kernel method (RKM) isn't very good. Based on this problem, we present the piecewise technique in the reproducing kernel space to solve this type of equations. The focus of this paper is to verify the stability and high accuracy of the present method by comparing the absolute error with traditional RKM and study the effect on absolute error for different values of α. Furthermore, we can study the distribution of entire space at a particular time period. Three numerical experiments are provided to verify the efficiency and stability of the proposed method. Meanwhile, it is tested by experiments that the change of the value of α has little effect on its accuracy.