Effective numerical simulation of time fractional KdV equation with weakly singular solutions-Reference-Cited by-同舟云学术

Effective numerical simulation of time fractional KdV equation with weakly singular solutions

Published:2024-04-30 Issue:03 Volume:15 Page:
ISSN:1793-9623
Container-title:International Journal of Modeling, Simulation, and Scientific Computing
language:en
Short-container-title:Int. J. Model. Simul. Sci. Comput.

Author:

Chen Hu¹^ORCID,Lin Xiaotang²^ORCID,Sun Tao³^ORCID,Tang Yifa⁴⁵^ORCID,Zhang Jingna⁴⁵^ORCID

Affiliation:

1. School of Mathematical Sciences, Ocean University of China, Qingdao 266100, P. R. China

2. Department of Statistics and Data Science, Faculty of Science and Technology, Beijing Normal University - Hong Kong Baptist University, United International College, Zhuhai 519087, P. R. China

3. School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, P. R. China

4. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China

5. LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China

Abstract

A second-order time-stepping method for numerically solving the linearized time fractional KdV equation (TFKDVE) whose solution has initial singularity is investigated. Alikhanov’s scheme is used to discretize the Caputo fractional derivative on temporal graded mesh, and the space is approximated by a Petrov–Galerkin spectral method. Detailed stability and error estimate of the full-discrete scheme are given, and the final error bound is [Formula: see text]-robust. Numerical examples are given to illustrate the sharpness of the error analysis.

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Ltd

Link

https://www.worldscientific.com/doi/pdf/10.1142/S179396232450020X

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