Numerical solution for a class of space-time fractional equation by the piecewise reproducing kernel method. Issue 10 (3rd October 2019)

• Record Type: Journal Article
• Authors: Wang, Yu-Lan; Jia, Li-na; Zhang, Hao-lu
• Is Part Of: International journal of computer mathematics. Volume 96:Issue 10(2019)
• Page Start: 2100
• Page End: 2111
• Publication Date: 2019-10-03
• Subjects: Piecewise technique -- reproducing kernel space -- space-time fractional equation -- Caputo fractional derivative -- approximate solution; Partial differential equations; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2018.1544367
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: 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.