Mixed Jacobi-Fourier spectral method for Fisher equation

Mixed Jacobi-Fourier spectral method for Fisher equation

In this paper, we propose a mixed Jacobi-Fourier spectral method for solving the Fisher equation in a disc. Some mixed Jacobi-Fourier approximation results are established, which play important roles in numerical simulation of various problems defined in a disc. We use the generalized Jacobi approxi...

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Bibliographic Details
Main Authors: Yujian Jiao, Tianjun Wang, Xiandong Shi, Wenjie Liu
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2018-04-01
Series:Mathematical Modelling and Analysis
Subjects:
Fisher equation in a disc
mixed Jacobi-Fourier approximation
spectral method
problem with end-point weak singularity
nonlinear problem
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/1417
Description
Summary:In this paper, we propose a mixed Jacobi-Fourier spectral method for solving the Fisher equation in a disc. Some mixed Jacobi-Fourier approximation results are established, which play important roles in numerical simulation of various problems defined in a disc. We use the generalized Jacobi approximation to simulate the singularity of solution at the regional center. This also simplifies the theoretical analysis and provides a sparse system. The stability and convergence of the proposed scheme are proved. Numerical results demonstrate the efficiency of this new algorithm and coincide well with the theoretical analysis.
ISSN:1392-6292
1648-3510

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