THE NUMERICAL SOLUTION OF THE TIME-FRACTIONAL NON-LINEAR KLEIN-GORDON EQUATION VIA SPECTRAL COLLOCATION METHOD

被引：4

作者：

Yang, Yin ^{[1
]}

Yang, Xinfa ^{[2
]}

Wang, Jindi ^{[1
]}

Liu, Jie ^{[3
]}

机构：

[1] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan, Hunan, Peoples R China

[2] Hunan Univ, State Key Lab Adv Design & Mfg Vehicle Body, Changsha, Hunan, Peoples R China

[3] Guangzhou Univ, Sch Mech & Elect Engn, Ctr Res Leading Technol Special Equipment, Guangzhou, Guangdong, Peoples R China

来源：

THERMAL SCIENCE | 2019年 / 23卷 / 03期

关键词：

caputo derivative; non-linear; time fractional Klein-Gordon equation; spectral collocation method; CONVERGENCE;

D O I：

10.2298/TSCI180824220Y

中图分类号：

O414.1 [热力学];

学科分类号：

摘要：

In this paper, we consider the numerical solution of the time fractional non-linear Klein-Gordon equation. We propose a spectral collocation method in both temporal and spatial discretizations with a spectral expansion of Jacobi interpolation polynomial for this equation. A rigorous error analysis is provided for the spectral methods to show both the errors of approximate solutions and the errors of approximate derivatives of the solutions decaying exponentially in infinity-norm and weighted L-2-norm. Numerical tests are carried out to confirm the theoretical results.

引用

页码：1529 / 1537

页数：9

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