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

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 equation...

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Published inInternational 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
LanguageEnglish
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
Online AccessGet full text
ISSN0020-7160
1029-0265
DOI10.1080/00207160.2018.1544367

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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.
AbstractList 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.
Author Zhang, Hao-lu
Wang, Yu-Lan
Jia, Li-na
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Snippet Due to the non-locality of fractional derivative, the analytical solution and good approximate solution of fractional partial differential equations are...
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SubjectTerms 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
Title Numerical solution for a class of space-time fractional equation by the piecewise reproducing kernel method
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